Pith. sign in

Paper Citation Record · LEDGER

Short Paths in the Planar Graph Product Structure Theorem

As of 11 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:2502.01927.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2502.01927 v1

Coverage vector

measured 60 of 60 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T14:12:32.949264Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

60 of 60 outbound references displayed

  • verified exact3
  • verified fuzzy33
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f71918a0-a7cf-447e-8f93-811c9da71e26 · outbound

This paper cites Characterization and recognition of partial 3-trees.

Short Paths in the Planar Graph Product Structure Theorem Characterization and recognition of partial 3-trees

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.584387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.736827Z digest=sha256:ad6bc68de59c9e21e1c28a09a419e4cf1907d7feb51bdca9210f45fa1cfb2c6c

Observation c51718db-631d-4a1c-b5d7-888c04b14037 · outbound

This paper cites Bekos and Luca Grilli.

Short Paths in the Planar Graph Product Structure Theorem Bekos and Luca Grilli

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.573639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.741248Z digest=sha256:0f3a7b192d9d9ea70cdd23451e150d092a192f140b20fb63502346e59334eded

Observation 5ac4cf7b-510d-4d1c-a558-933c0834bf4d · outbound

This paper cites Bekos, Giordano Da Lozzo, Petr Hlinený, and Michael Kaufmann.

Short Paths in the Planar Graph Product Structure Theorem Bekos, Giordano Da Lozzo, Petr Hlinený, and Michael Kaufmann

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.562213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.745183Z digest=sha256:90503ef36dd01ff966d23d34171bd90c784008f3773d37550842517b10e007ee

Observation d7ac67e8-bd77-4b75-baf7-d24bff49cabc · outbound

This paper cites Drawing planar 3-trees with given face areas.

Short Paths in the Planar Graph Product Structure Theorem Drawing planar 3-trees with given face areas

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.748964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.748964Z digest=sha256:efd9830c20ba60b67fc4f8c132c996b99caf18874e240101b194a096ed0bf7d8

Observation 939d2b5d-2d13-4bfc-9b3f-f07bd12ffbad · outbound

This paper cites Bodlaender.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.542963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.752914Z digest=sha256:27ddd12b1d7e87d4648688cfd331213ee0996de1821e16579146a2a38d70063e

Observation fcb5ddda-e49d-412d-b112-ef67b61d5169 · outbound

This paper cites Bodlaender.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.532166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.756728Z digest=sha256:c12d3441537fbce157feb3aa4e1e06adda3aefbb3e19da78e9e0a1f7bd338c66

Observation 5143fc20-ee43-48a8-bd0b-1a83369f352a · outbound

This paper cites Bodlaender and Joost Engelfriet.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender and Joost Engelfriet

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.521811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.760520Z digest=sha256:f4b3cf0ea40a4178fe2fbb67bd8d02d8ece4af11ba9175324dfdd8aa109196ad

Observation 72dcd3c8-68ec-4287-9f2f-7af741f6e66d · outbound

This paper cites Bodlaender, Carla Groenland, and Hugo Jacob.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender, Carla Groenland, and Hugo Jacob

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.511143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.763701Z digest=sha256:265f2e005ea2cbe69e098416b035b83a54c304307e987df72335a78dbe22163c

Observation 7d9f29bd-ab3d-40ab-a62b-4c2c9eb3c651 · outbound

This paper cites Shorter labeling schemes for planar graphs.

Short Paths in the Planar Graph Product Structure Theorem Shorter labeling schemes for planar graphs

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.499797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.767097Z digest=sha256:39f3b03057c06772dddd32b6fa6b2cd16c30791d9de75fa591b3536347aac454

Observation f7864373-8b61-493d-a01d-9b9d079437e5 · outbound

This paper cites Pruessmann, Anusch Taraz, and Andreas Würfl.

Short Paths in the Planar Graph Product Structure Theorem Pruessmann, Anusch Taraz, and Andreas Würfl

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.489623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.770118Z digest=sha256:4d7bf60ad504d36df20963d80afe9b6e2b90078392c6aa76d87a6775a5dc283f

Observation 4b7815b4-6bfc-4ff6-b115-2dc881d13ba6 · outbound

This paper cites Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, and Da vid R

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.478720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.774372Z digest=sha256:57e5bdd323405b7ac3a4c0b370e85aaed87163e450bf82fabc2920cc8870c98f

Observation ffc35aab-c05f-4553-a1b3-3020bcae9557 · outbound

This paper cites Apollonian ball packings and stacked polytopes.Discrete Comput.

Short Paths in the Planar Graph Product Structure Theorem Apollonian ball packings and stacked polytopes.Discrete Comput

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.468242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.777436Z digest=sha256:1728c250669f956d88a13c38c426b6bb1c73f19cd9cca573588a07c2c83e468e

Observation eadffa25-3b2a-44ef-a7d4-63ee52986baa · outbound

This paper cites The thickness of fan-planar graphs is at most three.

Short Paths in the Planar Graph Product Structure Theorem The thickness of fan-planar graphs is at most three

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.457922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.780592Z digest=sha256:ae8d4f7ef5a591d16f28e39cf1d5efbff041ad4d62ac24531ab7e33a6eb2f364

Observation bb67acd3-4ef4-441f-880c-a9bb8bea82a2 · outbound

This paper cites Some results on tree decomposition of graphs.J.

Short Paths in the Planar Graph Product Structure Theorem Some results on tree decomposition of graphs.J

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.784718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.784718Z digest=sha256:b44d905dc0abbd3428ffad13c965180e7d1ac26659b28408fb54984c070fa68b

Observation c8b9e675-a5f1-499a-ae7f-286290a15552 · outbound

This paper cites On tree-partitions of graphs.Discrete Math., 149(1– 3):45–58, 1996.

Short Paths in the Planar Graph Product Structure Theorem On tree-partitions of graphs.Discrete Math., 149(1– 3):45–58, 1996

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.441255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.788369Z digest=sha256:718b028d646d4ff06071d0c1fec01da71b9f870717aa4a4e6a4fb6dd6c97e053

Observation 49a54fbe-3d8a-4612-a267-29a8962981eb · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.430958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.792220Z digest=sha256:04901e4914d38a3f3d19327188e8381daebe69f65fe56621052298b66308c328

Observation a58e5913-b432-40ff-ab57-c21c4b33c4fc · outbound

This paper cites Seweryn, and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Seweryn, and Da vid R

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.420739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.795826Z digest=sha256:92ff4f6052e3468dfb73d2e8052a55c53e593e074edf68406115a5ab224fe45c

Observation b5ff7e97-fba7-423a-ab94-24d0f3d78942 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.409251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.799232Z digest=sha256:113a94aab780d5304dfcfe1b27ddd61d04885265e2fe814b5264c612cae2611e

Observation ed019191-15d1-4ac8-9488-f9806c58f0e4 · outbound

This paper cites Improved bounds for centered colorings.Adv.

Short Paths in the Planar Graph Product Structure Theorem Improved bounds for centered colorings.Adv

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.398748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.802781Z digest=sha256:0cb2694a07dc70baefc327b86485c91a5121f6e424e5d505359e6aefabe36d69

Observation 12095158-f9b9-4f93-ae31-1686b7eaf1c1 · outbound

This paper cites Size-Ramsey numbers of structurally sparse graphs.

Short Paths in the Planar Graph Product Structure Theorem Size-Ramsey numbers of structurally sparse graphs

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.806261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.806261Z digest=sha256:fd39a26a9a6f96760f20a8c01f49d2e2d1ced609c1f4c181d7de8a846ee366dd

Observation 56aa0325-141a-459e-950f-a63e84803a93 · outbound

This paper cites Adjacency labelling for planar graphs (and beyond).J.

Short Paths in the Planar Graph Product Structure Theorem Adjacency labelling for planar graphs (and beyond).J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.387893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.810178Z digest=sha256:a65d54b088e5aa7c0b069c80f648346a4fbffab5176362ccdf036b797a9c0c54

Observation f6c622df-fc00-4b7e-8051-037018d5887b · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.377561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.813424Z digest=sha256:ce976d96df8d9cf7a72875cedf3d2b9fe66e05d4824707b0b9c614bb9cdbbd87

Observation 5a5f893f-d780-4feb-8ec8-9e40b73a2afd · outbound

This paper cites The grid-minor theorem revisited.

Short Paths in the Planar Graph Product Structure Theorem The grid-minor theorem revisited

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.817196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.817196Z digest=sha256:f55c7bb0a1f7108b1536141d71a0d3d45896d6985b191b810a77af61dcb6f78e

Observation 1d786411-04bf-44a2-8715-fa8194961578 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.366291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.821169Z digest=sha256:a518873aac7683652454f3d61394e85416492e740fd4628ec41c099526ab9535

Observation 13c88c4a-d05e-4fa1-904f-54c91fea6bf9 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.355685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.824315Z digest=sha256:e21bce2c003fc28d68e74274923b5dc8211cb5338fb6f7297f84a27eb686f9d4

Observation a621474d-992c-425f-8a79-598098a2f505 · outbound

This paper cites Layered Separators in Minor-Closed Graph Classes with Applications.

Short Paths in the Planar Graph Product Structure Theorem Layered Separators in Minor-Closed Graph Classes with Applications

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.827700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.827700Z digest=sha256:a2c3cef518e4215889aa0f3993e2b921c57e4fee6613dbaad9286d3445eaa0ed

Observation 98b84c24-5577-442e-a6a1-26abe1772690 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.344353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.831494Z digest=sha256:29aab55e23030c0bd7bead2701102da88b26ff52d4ef79fe4c72f99ad2cccbdc

Observation 2d54a038-107c-4b82-aac6-c7dc62273857 · outbound

This paper cites Grid Minors and Products.

Short Paths in the Planar Graph Product Structure Theorem Grid Minors and Products

Reference 28

Resolution
metadata mismatch
local_arxiv, observed 2026-08-09T14:12:33.058193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.834751Z digest=sha256:e82705a536c5045a23978700dcbddd49f0daca967c11b111662bb62dcfd1f009

Observation bd6f5483-ce8e-432f-b308-9752ca2c497b · outbound

This paper cites On comparable box dimension.

Short Paths in the Planar Graph Product Structure Theorem On comparable box dimension

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.333980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.838362Z digest=sha256:3d3ddd572c506116130aecade38d1f1a07dd986e2e8611e12385c2b65d52f38a

Observation 82d203d2-1c28-4fc9-aeb0-9e2aeb7f1d76 · outbound

This paper cites On fractional fragility rates of graph classes.

Short Paths in the Planar Graph Product Structure Theorem On fractional fragility rates of graph classes

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.323669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.841671Z digest=sha256:6d615f93adc8a1a0beeddb725ec4965a546ac75dfecfc80a4a9845b4e804d6d7

Observation 4542b8f9-70b5-4db9-8d5f-c57384e53faf · outbound

This paper cites Quotient tree partitioning of undirected graphs.BIT, 26(2):148–155, 1986.

Short Paths in the Planar Graph Product Structure Theorem Quotient tree partitioning of undirected graphs.BIT, 26(2):148–155, 1986

Reference 31

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.844997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.844997Z digest=sha256:493e602848910c785a36f644172ab7a6d6a07bb670728cd0036f6e55a1479ab0

Observation a463c5c4-ebe1-4242-bd0e-e2e7d43bd883 · outbound

This paper cites Subgraph isomorphism in planar graphs and related problems.

Short Paths in the Planar Graph Product Structure Theorem Subgraph isomorphism in planar graphs and related problems

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.307576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.848566Z digest=sha256:32e0dabc9886cee44495f946a82cf965d4822898376b95a232aca00c93b0e7d6

Observation abb18c7c-9f69-4d76-86fa-acdad2f060b4 · outbound

This paper cites Sparse universal graphs for planarity.J.

Short Paths in the Planar Graph Product Structure Theorem Sparse universal graphs for planarity.J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.297510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.852552Z digest=sha256:2050d6ba53aba9119aba34f8ee7cc3c3d06cc241934acffa73e88651f940ea2f

Observation 1d981d9d-c635-44df-bfc0-c0a1fbaffdb4 · outbound

This paper cites Tsourakakis.

Short Paths in the Planar Graph Product Structure Theorem Tsourakakis

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.286449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.856040Z digest=sha256:4f7cb34915c8bd4758014ccd74c6b76bd20ddb6c32c1979da30925386f489cb9

Observation 20daa068-dcad-4197-acc2-60ade515c299 · outbound

This paper cites 3D-grids are not transducible from planar graphs.

Short Paths in the Planar Graph Product Structure Theorem 3D-grids are not transducible from planar graphs

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.859835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.859835Z digest=sha256:1249019938410d06984281613c4b32fbcb3478545c56a8c181063de41af2910d

Observation e79d201d-11a0-4fc1-afd6-d6212e942f11 · outbound

This paper cites Simpler adjacency labeling for planar graphs with B-trees.

Short Paths in the Planar Graph Product Structure Theorem Simpler adjacency labeling for planar graphs with B-trees

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.276310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.863822Z digest=sha256:34b00f59de9297c1de2b08ee28c29469aa0e681494869cb4b8355ff651b15de2

Observation aaa38288-a7d5-4c3f-bb9b-605e9bd33d0b · outbound

This paper cites Tree-partitions of infinite graphs.Discrete Math., 97:203–217, 1991.

Short Paths in the Planar Graph Product Structure Theorem Tree-partitions of infinite graphs.Discrete Math., 97:203–217, 1991

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.867194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.867194Z digest=sha256:c6eb9fb52378c0355a5679f18b059a125f6ae5fdc8de8094d64048663e9da415

Observation 9c7f1ee5-6d16-46a3-8795-c17ad451dc0a · outbound

This paper cites Har vey and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Har vey and Da vid R

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.259224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.870346Z digest=sha256:c34ee5bf8b0babc9b82285f055920898c71e0d7273cc3bbfd04d3c7d5e94e412

Observation 39810498-6eb4-45f9-b2b3-1793c5531909 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.249523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.873767Z digest=sha256:97c62372d76221adad3fc71a18b34a357f8c3c14ce27412e906960fc567b6dc5

Observation 3f406323-5f4a-4f19-a4f4-71daf75628ec · outbound

This paper cites H-clique-width and a hereditary analogue of product structure.

Short Paths in the Planar Graph Product Structure Theorem H-clique-width and a hereditary analogue of product structure

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.239407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.876973Z digest=sha256:3bf891c57a89e554f140bcf4b132de4843509c9f4f4e1bf710123dfe55ad0a06

Observation 13f05797-34c6-44e2-8c6c-8321dae86f37 · outbound

This paper cites Transductions of Graph Classes Admitting Product Structure.

Short Paths in the Planar Graph Product Structure Theorem Transductions of Graph Classes Admitting Product Structure

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.881181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.881181Z digest=sha256:daa3007b236e596882728f825579c5dde6dbbcad24d53d45a8ade55396f3fa84

Observation 721133ca-65a9-4ec9-b443-d94f638e55db · outbound

This paper cites Universality in minor-closed graph classes.

Short Paths in the Planar Graph Product Structure Theorem Universality in minor-closed graph classes

Reference 42

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:33.025914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.885752Z digest=sha256:c05268b7aafaea90d8ed05cd0b46f9401c19223226a0514bacb75f63691baf98

Observation e8ce47b2-6196-4ac0-aaaa-d543dc06d052 · outbound

This paper cites Product structure of graphs with an excluded minor.

Short Paths in the Planar Graph Product Structure Theorem Product structure of graphs with an excluded minor

Reference 43

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:33.011804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.889428Z digest=sha256:fce64aa85ae7843ec826f0422a66d0489c00b512206d1f0574948ca2d440c44e

Observation d538f02a-2c80-4d5a-b9cf-84cdc1eee677 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.229227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.893680Z digest=sha256:410db56fc65235c899cbb1aedce73211a0775fb89244d19304df34e531224ea4

Observation 6c42231b-d842-46ab-94e9-8ae059c0da42 · outbound

This paper cites Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs.

Short Paths in the Planar Graph Product Structure Theorem Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.219012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.897047Z digest=sha256:0ccaf093b4a00336338e1adf8ddfcc3b678d54306c9267677dffed7d0af6d9ff

Observation bdbc4a97-4a19-4c21-9073-545c446ee6c2 · outbound

This paper cites The density of fan-planar graphs.Electron.

Short Paths in the Planar Graph Product Structure Theorem The density of fan-planar graphs.Electron

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.208180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.900400Z digest=sha256:efbdc4d349480e18a3256643d1e2ec5781407c463a7fd32d5fb1b4411fb5c91d

Observation 8887926b-8369-46cd-97c3-72dbb67e6993 · outbound

This paper cites Simple treewidth.

Short Paths in the Planar Graph Product Structure Theorem Simple treewidth

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.197580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.903787Z digest=sha256:2d83e01c18debad7439db731600389b75b61ad47f7630d5837d426be01aa3024

Observation f0f89812-c2b4-4717-9a18-962be72ed0b8 · outbound

This paper cites A note on planar partial 3-trees.

Short Paths in the Planar Graph Product Structure Theorem A note on planar partial 3-trees

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.907455Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.907455Z digest=sha256:1981355c8ec5055912cf62687459ded63029956ab5d546cba2247d3b1e8f5e3c

Observation 2e8fb341-3796-42dc-88fd-99ef873b8812 · outbound

This paper cites Twin-width of graphs on surfaces.

Short Paths in the Planar Graph Product Structure Theorem Twin-width of graphs on surfaces

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.187733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.911195Z digest=sha256:322ba27e3d0d651ef00537154ef58241c9c45565e4de1cfc7341bec1c7f81cd1

Observation c3081497-fe0e-45f9-a9c7-af01c4f95d6b · outbound

This paper cites Paciornik.

Short Paths in the Planar Graph Product Structure Theorem Paciornik

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.177179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.914500Z digest=sha256:a8d1889c61b0cf621708adafd94a254064ca6dd686767ad47c20e69612108e6a

Observation d28915ec-0260-48f6-8613-23b50db74f8d · outbound

This paper cites Graphs drawn with few crossings per edge.Combinatorica, 17(3):427–439, 1997.

Short Paths in the Planar Graph Product Structure Theorem Graphs drawn with few crossings per edge.Combinatorica, 17(3):427–439, 1997

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.166808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.918522Z digest=sha256:853c031d50cb58428eabd99fa194a652aac4cab6ae9624ce3ef626af3dfe621c

Observation 1196c5e5-ac31-466a-8b6b-bda358dfaa1a · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 52

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.921749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.921749Z digest=sha256:c5072d382803d0cee237db7ecfebf3c066f63ad1333e53a870dc986c31350c3e

Observation e4b8ae72-a0f7-4f45-ba90-87b26eb61f5c · outbound

This paper cites Tree-partite graphs and the complexity of algorithms.

Short Paths in the Planar Graph Product Structure Theorem Tree-partite graphs and the complexity of algorithms

Reference 53

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.925162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.925162Z digest=sha256:9f60c9da8ad14da6c5cd7f94041f8eaf17392489a96e5e8f042bb700b1610d1e

Observation 84a71c30-aff1-4166-b72f-205ab2fb0030 · outbound

This paper cites Graph searching and a min-max theorem for tree-width.

Short Paths in the Planar Graph Product Structure Theorem Graph searching and a min-max theorem for tree-width

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.928609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.928609Z digest=sha256:24567344d22572e76802f9d9509a7fad8330e1e25ecf2590d882cbbce921fa4d

Observation 489a027c-0e3f-4b33-8be2-0deadf29adc4 · outbound

This paper cites New representation results for planar graphs.

Short Paths in the Planar Graph Product Structure Theorem New representation results for planar graphs

Reference 55

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:32.985770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.931986Z digest=sha256:ba8b2f342cdb209eb845d23965b39e122b567f00e7412901c54156092878d264

Observation 543a19be-2233-4dad-92ba-db2f42c6c9bf · outbound

This paper cites Wood, and Wendy Yi.

Short Paths in the Planar Graph Product Structure Theorem Wood, and Wendy Yi

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.137279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.935576Z digest=sha256:df501a304705e9294d7dd700a3edc574f338323977102be55c3942682dcf8e65

Observation bbf934f6-437a-4701-ba55-f2c986b67574 · outbound

This paper cites Geometrie der lage.

Short Paths in the Planar Graph Product Structure Theorem Geometrie der lage

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.127104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.938775Z digest=sha256:8b5e70063ddbb7d904c30c5f0f08bd7237e6cd7f579132376e75dad2be01f8a1

Observation de8ab704-2cee-4960-b73e-2d2f34338a59 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.116833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.942247Z digest=sha256:3f277df35d3feab4e78befccab42c0c3e88b01fb2fc9e131949c4b23dda7c375

Observation 3b70dce9-fde0-448f-b411-1c30ea667c84 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.106686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.945858Z digest=sha256:d17c38ff0d7f4cd82d010b2c446bd1834915811e4a8ce51e207ec1deee9c9671

Observation 723b3ed3-4429-4738-a629-134ddff02ee6 · outbound

This paper cites Stacked treewidth and the Colin de Verdiére number.

Short Paths in the Planar Graph Product Structure Theorem Stacked treewidth and the Colin de Verdiére number

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.096725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-09T14:12:32.949264Z digest=sha256:6846a37df3fda2107994627c92be500efcdd2c555b5ce028f8de36df93953425

Pith citing papers

No inbound Pith citation observations are available.