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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 2026-08-11T06:34:44.6726+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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.736827Z digest=sha256:660029b17503a445e2d56bdff879f033a6cec8e37a3c6b9b66077abd187db882

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.741248Z digest=sha256:676cab2bfa103684e70dc685ffbfcd73559e55e532017a19d0a5bb651a6c39a6

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.745183Z digest=sha256:f2c312e79281a87c58a589c077bdd34ba93863e7f14238967d371e9d2c46e0af

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.752914Z digest=sha256:f805836e0a9ad9abec97453bbac232bc5fddab8f1aaa5777aaa111e2d06d0eaa

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.756728Z digest=sha256:a5e2338bcabd0098ad64f5b0c42c151d54b2d7b771a38332b7ab57cc908c86e8

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.760520Z digest=sha256:adc1a6f4c956ea172c71d6bbe6d744266d639a20fb3f15fd9450bb03e36fc9c7

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.763701Z digest=sha256:ffbe13f6c8eacf62532efbf89b98339d959a554ad7c42e58629ebcb6b839fa7f

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.767097Z digest=sha256:13e3b4c6af240738834e960afc89d9ed90e19e4ed6f5099db1f88aa79d3434d1

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.770118Z digest=sha256:21b77fcb729342d7becdbcf80a84bbb61912f1e8aab1fa1ddf8473049d797c65

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.774372Z digest=sha256:08fe3903d811f0a7e5d542c48e4b70d3a6bece596af650e2fe3cf14febca4c78

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.777436Z digest=sha256:c2383ff737b051226a3671a3d5958ae6094a4a1cf0eddff0a9903d9149e7a904

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.780592Z digest=sha256:91558878508f3a38cbcd8029a94c9d2ec7ee015df763cf100c2bcdd9cafcb0b8

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.788369Z digest=sha256:affb4eb3e98da98994f4c0a29f2e56f88e8fa0e9b5ec920e8e808a5dcf40500e

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.792220Z digest=sha256:342d08b88af022dd8ee9fe230c7e7b6df721dc45479fe6e4be94a2c4a71d34d5

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.795826Z digest=sha256:b8323611e8c4c46d7710876b726dfd82426c6d1aa37aaaab5070158626bab425

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.799232Z digest=sha256:7d103eb295688eeb28ac5594d1c6c23fa75af9ef9edcefe7fe59614efd6d4d44

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.802781Z digest=sha256:fe4157c5e930f0587c411e121d3ff0372e7d8ac9a2c232abbbf38d02e2f01383

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.810178Z digest=sha256:2c31ea958a730660e28722dff616ef6c07e2abe8d545c0ce6bc5a49ebf89e2d2

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.813424Z digest=sha256:f86b59d6ba1530a4d702715b087778b20fda761e92ac5bf3d41d1f7b6f18168d

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.821169Z digest=sha256:e88ebc157d26e88f12e4ba9d12650550a1dc334f413371cd5a462ec9877218f9

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.824315Z digest=sha256:4d95d40093bd9c6ea42d4914c86fc48d9b7389bfb09ed1ce6eee3bd66af5f2fe

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.831494Z digest=sha256:695c655dd70debf33982c222ca1576bec6c1a9c05fb68ffbff4b282c41599312

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.834751Z digest=sha256:edce71f207dbf1490a5b979be672ac919fc4eaebe098b8d02ae83f797de05fa9

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.838362Z digest=sha256:d98962a661919d65895b2836ddc4c86393f62c12417bbad60941ad6b10a9f511

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.841671Z digest=sha256:c905b4f83dd95c7ddcf7dd52f3f1eb36c6fa333ea6cead007e830bb7b188e6c2

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.848566Z digest=sha256:c565561f9003385850f304d80b71df0669b5ef5279c61ec51e88887d0574ca0e

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.852552Z digest=sha256:8ba784a62d7930be4f96a1f595a68b08f595779600ac71919b3bc6b82c211474

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.856040Z digest=sha256:a52472321bb26fec98298c0c34979270b7ff2249145771c65564670c8276713e

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.863822Z digest=sha256:0b44503cdf5137f5f911dabbd39ebea533a8967ed7728ef48169df28929a2c51

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.870346Z digest=sha256:f4d6021559652c6070ea8ac17f69f2af40ce7c3a7373b859155c22cee50bcffe

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.873767Z digest=sha256:ff277927f7f290886ac91d2305ad4c7c9ab612c273b287b4f77aa472fb1c1739

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.876973Z digest=sha256:1a48607fe499b3ebc4758513d7280d6cfa5478e6351afc8547dbfab03a726140

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.885752Z digest=sha256:1e7787b934f29b0a530e158391f0528c96ed07e42d2a7e496a1cc5bd3d5f4072

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.889428Z digest=sha256:16f9fe7cbc2a4c515c931afe37fbafe4daddceccf63c58f14fd65b92f6f910db

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.893680Z digest=sha256:5f2156b98c22fb78ef4f0d126b44b4779bcd4152f8a958a3569ede63435420fd

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.897047Z digest=sha256:9a3da6902a617a0d4827a105995e6fdcb4e2a4d0cf7653c5cf073a2af4da3a8e

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.900400Z digest=sha256:cd3480dde0af39d1e21ebe38cd1e03358a1e21789b5f55056f0bb37201951c8a

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.903787Z digest=sha256:7373c633051da2e9ffac2adf05fcfc7941fffc9f798355afa9223a14e05a4664

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.911195Z digest=sha256:0c662bd2f16e8ef05f09c8f9b85fd1b1579aa6394b96ed72d79f9e6e93fecff7

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.914500Z digest=sha256:43dde74298acc84e2fc489cfe3141b9ea303b34a582373fa3bf057cef4c7e2b0

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.918522Z digest=sha256:11e5019d6bf4fc3b2d5432d3fd23fbb0fb61049824d200f04af6a42a29b85da9

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.931986Z digest=sha256:15c09c3fbadd4aeb9a62d0fa1ac84a7f86670198f48730ec87e27138056d881f

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.935576Z digest=sha256:a34958afc6b7b38609f71fb1d108152d17541b62263fc9a4d751171ebdafcbe7

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.938775Z digest=sha256:4233f5c85e718bcec662a2fed6c2aeee1821206c2fad85b7c7fd10654a079a32

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.942247Z digest=sha256:23a3fc9d20d00470b56aa16a9c868a5275b7ba81454b4770a1116be7bdb64a24

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.945858Z digest=sha256:6d9fe262c4019dbf33cfa87e97be7f96652918ad52e89d1ff1de0539796265d0

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-09T14:12:32.949264Z digest=sha256:35ec0db3c2430a54006859a0f3eab0cac69af780f7f8108bbd31ec06cfe884bc

Pith citing papers

No inbound Pith citation observations are available.