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Paper Citation Record · LEDGER

Simultaneous Representation of Proper and Unit Interval Graphs

As of 16 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:1908.08882.

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

pith.paper-citation-record.v1
1908.08882 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:39:30.123290Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

30 of 30 outbound references displayed

  • verified exact16
  • verified fuzzy3
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fbddf600-53a6-4e58-bfe0-6ca3768a0875 · outbound

This paper cites On some NP -complete SEFE problems.

Simultaneous Representation of Proper and Unit Interval Graphs On some NP -complete SEFE problems

Reference 1

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.475177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:29.951457Z digest=sha256:3e91d0054be87b9af2c227f600985d79ab6e84a920f7376b4667848e8cec78f0

Observation 9c4af839-9eca-4c38-a42a-366c06612573 · outbound

This paper cites Plass, and Robert Endre Tarjan.

Simultaneous Representation of Proper and Unit Interval Graphs Plass, and Robert Endre Tarjan

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:29.958408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:29.958408Z digest=sha256:ff8f8dbf358e1dd56763f44762ae0124b8f948374c5ce5bc044f12b8b1146dbf

Observation a999211f-3211-43c3-b3da-c34781cdb16f · outbound

This paper cites Simultaneous Embedding of Planar Graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Simultaneous Embedding of Planar Graphs

Reference 3

Resolution
metadata mismatch
local_arxiv, observed 2026-08-14T11:39:30.651569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:29.965500Z digest=sha256:01d6d2a9a07242eec82ffe9d24442f9ab853f3b1b1b80c5d3efc6381a0d92ee6

Observation 8f3e9f79-4669-460a-b497-195387c8638e · outbound

This paper cites Simultaneous PQ -ordering with applications to constrained embedding problems.

Simultaneous Representation of Proper and Unit Interval Graphs Simultaneous PQ -ordering with applications to constrained embedding problems

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:29.971279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:29.971279Z digest=sha256:a78556d5beba10bf82e6a259a7f3f9ad38f34436d6c27e54200fb859c16056d5

Observation 4ba869dc-3f91-4c80-9459-056a0ce64611 · outbound

This paper cites A note on simultaneous representation problem for interval and circular-arc graphs.

Simultaneous Representation of Proper and Unit Interval Graphs A note on simultaneous representation problem for interval and circular-arc graphs

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:39:30.626917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:29.978997Z digest=sha256:2d80741d4bade6f8ebcd8daa8ddbf6348b43cbedf56d5125d44d083ac51c3b27

Observation d7b19fba-a0cf-4f67-977e-e8b1d321d620 · outbound

This paper cites an unresolved cited work.

Simultaneous Representation of Proper and Unit Interval Graphs Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:39:30.758221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:29.985462Z digest=sha256:f9c2bb10f1a20ae7b2e4d06997497c54372a322956a1207672c7c2cea449d7f5

Observation 3bd99a0e-9f94-41a6-acf5-96bb5583c8da · outbound

This paper cites Booth and George S.

Simultaneous Representation of Proper and Unit Interval Graphs Booth and George S

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:29.991629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:29.991629Z digest=sha256:7ebace40a3b5237bace7872403fb18ffa17f98b07ec77cae75b41261c4c34e17

Observation 494cf820-fab8-4ea1-b781-fe96a71d9572 · outbound

This paper cites On simultaneous planar graph embeddings.

Simultaneous Representation of Proper and Unit Interval Graphs On simultaneous planar graph embeddings

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:29.997805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:29.997805Z digest=sha256:3bdf5ec089e1dc6d7fc889d00c9f78c59e41e7835a7a14d091acce19c2733729

Observation 7b5e4263-052b-4b97-94da-9d2c863c07b6 · outbound

This paper cites Extending partial representations of circle graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Extending partial representations of circle graphs

Reference 9

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.412957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.003269Z digest=sha256:19297f0ed84c804a36d9a8744aee68d99b2490986af19d1469f9ef08a0c471e6

Observation 6ea33f86-3fd3-4ffd-aa6d-abb9bcad9513 · outbound

This paper cites Herrera de Figueiredo, João Meidanis, and Célia Picinin de Mello.

Simultaneous Representation of Proper and Unit Interval Graphs Herrera de Figueiredo, João Meidanis, and Célia Picinin de Mello

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:30.009718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:30.009718Z digest=sha256:1d6ab020191bd0f108e1b54228b149709f9d65ffac0280d94c9bedbd07731f93

Observation 2027bbcf-95af-4bd7-a839-4782e5cbad7e · outbound

This paper cites Linear-time representation algorithms for proper circular-arc graphs and proper interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Linear-time representation algorithms for proper circular-arc graphs and proper interval graphs

Reference 11

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.384105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 8d4073a4-ad44-443e-9749-6be6e836988f · outbound

This paper cites Simultaneous geometric graph embeddings.

Simultaneous Representation of Proper and Unit Interval Graphs Simultaneous geometric graph embeddings

Reference 12

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.367059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.020691Z digest=sha256:39b3859660f10556accb6b4fdb702e1b9fd3525fcb6fecf379bf14349d0b2cd5

Observation 3a65b4c8-e236-4204-8e92-350839f5e0d4 · outbound

This paper cites Simultaneous graph embeddings with fixed edges.

Simultaneous Representation of Proper and Unit Interval Graphs Simultaneous graph embeddings with fixed edges

Reference 13

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.349521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.027849Z digest=sha256:82767365550dbfa357ef2a5855a8b5c8c3f5f7348425384d5463c25600718d88

Observation e849145f-02bc-4496-88e4-0a6d897d6c05 · outbound

This paper cites Goldberg, Martin C.

Simultaneous Representation of Proper and Unit Interval Graphs Goldberg, Martin C

Reference 14

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.332045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.032978Z digest=sha256:3c7e5a56c2694fdd4a733d683909f2c148680c8e1e402b78eda153c35b5bff60

Observation e9fc0aa6-b453-40e4-ad47-da68f9749beb · outbound

This paper cites Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57).

Simultaneous Representation of Proper and Unit Interval Graphs Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:39:30.741152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.039110Z digest=sha256:d921833585ba87883bb9ecf81be80afc1bc546694cc41e32ba9ba3493d84b4f6

Observation 5009937a-0066-4a28-8a44-d432fa7273b6 · outbound

This paper cites Graph sandwich problems.

Simultaneous Representation of Proper and Unit Interval Graphs Graph sandwich problems

Reference 16

Resolution
verified exact
raw_fallback, observed 2026-08-14T11:39:30.602718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.044353Z digest=sha256:49a21f96fabca497a9d92f794e55b351294f2aa17555ae3a53fc224d767b18db

Observation 3619bc5f-df5e-47f4-8f44-c89c9660fbed · outbound

This paper cites Induced subgraph isomorphism on proper interval and bipartite permutation graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Induced subgraph isomorphism on proper interval and bipartite permutation graphs

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:30.049516Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:30.049516Z digest=sha256:6cc412c5e8341b7a73f2234a83c9a50c91e2b4ccb355ec9caab7d2524c37faba

Observation 93556ffa-7def-4b10-8a95-7980632459c9 · outbound

This paper cites A fully dynamic algorithm for recognizing and representing proper interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs A fully dynamic algorithm for recognizing and representing proper interval graphs

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-14T11:39:30.054634Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-14T11:39:30.054634Z digest=sha256:e190922b1c72a461568a73a69d0c628c3ea969396eeefe100f9d703bb3810ecc

Observation 1e5af80a-8b94-4e7f-8380-3e62276aa17f · outbound

This paper cites Simultaneous interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Simultaneous interval graphs

Reference 19

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.290927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.060298Z digest=sha256:f53c5fadf2a6413675dbe0ac42898655038f75faff157668f8b86faf199853a0

Observation 2be721b1-e8e0-4c8b-be47-e4f470501d2e · outbound

This paper cites The simultaneous representation problem for chordal, comparability and permutation graphs.

Simultaneous Representation of Proper and Unit Interval Graphs The simultaneous representation problem for chordal, comparability and permutation graphs

Reference 20

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.274216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.065364Z digest=sha256:be634bf4e87034ba91de44c2b3656fad7096330375233c661bbbf1546651b88b

Observation e5e14f5d-8a9b-4a1a-a5d5-39bf33fde4ce · outbound

This paper cites Extending partial representations of proper and unit interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Extending partial representations of proper and unit interval graphs

Reference 21

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.255251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.070842Z digest=sha256:de93462dca9bad8ef001512bb25119a1713195e49f54679ec12bb4f3d781c454

Observation c69e1d3a-0552-45b1-a81b-6a4b1eedba5c · outbound

This paper cites Optimal greedy algorithms for indifference graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Optimal greedy algorithms for indifference graphs

Reference 22

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.237113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.076303Z digest=sha256:7da820c68d9d24dd40d9bcc5276f28a0fd1cfbe15c2c9bdd3865600411a8e2fe

Observation 4749d372-e623-476a-bb8a-f69ad74581da · outbound

This paper cites Linear-time recognition of probe interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Linear-time recognition of probe interval graphs

Reference 23

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.220500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.081489Z digest=sha256:f1c010770e52e7044ecb3ec6d97ec05e60ac41841b959d221360d9e3ed3c9f06

Observation 7d82ba2d-617f-4880-9104-2e69377126d4 · outbound

This paper cites Recognition of probe proper interval graphs.

Simultaneous Representation of Proper and Unit Interval Graphs Recognition of probe proper interval graphs

Reference 24

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.204470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.087889Z digest=sha256:cb32cfb6678be3a9f584e98a627ffe6814e08d3799c42a57e4c7972888a9ac98

Observation fd02d4e6-c099-45be-b567-223efc555161 · outbound

This paper cites Total ordering problem.

Simultaneous Representation of Proper and Unit Interval Graphs Total ordering problem

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:39:30.723470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.093650Z digest=sha256:2038bfc9b7e09f8a7c64981437d9d0071f55719ad527185687259914741a0bbd

Observation fba05365-fe6b-46f9-b15a-1d44da1bd1d2 · outbound

This paper cites Representations of indifference relations.

Simultaneous Representation of Proper and Unit Interval Graphs Representations of indifference relations

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:39:30.706472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.098925Z digest=sha256:cc427c09e05e01775437a12734ac4fedf6a0ccba0f9a814bb5245b8a51cea159

Observation 8ebd361f-b8bb-4030-b10c-c6595101afb5 · outbound

This paper cites an unresolved cited work.

Simultaneous Representation of Proper and Unit Interval Graphs Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:39:30.687391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.106807Z digest=sha256:4576486bc882deb1356d063a874c2e8c5e7165f56822b2bce111c135e515fade

Observation f18fe4ff-aab6-4693-bedd-45e927c4593c · outbound

This paper cites Toward a theory of planarity: Hanani- T utte and planarity variants.

Simultaneous Representation of Proper and Unit Interval Graphs Toward a theory of planarity: Hanani- T utte and planarity variants

Reference 28

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.185905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.112099Z digest=sha256:b0b0b4f08e4d883def6daf3fef70429eac7ed66aea296dc1a1298f93e5005b07

Observation be7cd0fc-3366-402a-90f3-d954dce11971 · outbound

This paper cites an unresolved cited work.

Simultaneous Representation of Proper and Unit Interval Graphs Unresolved cited work

Reference 29

Resolution
verified exact
doi, observed 2026-08-14T11:39:30.164532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.117826Z digest=sha256:600e10d21d856aa72175b23b22f16b95103fe25f8e57d7417988e64d08dd2db6

Observation a389851c-3304-412a-b9e6-4300361c5f9a · outbound

This paper cites an unresolved cited work.

Simultaneous Representation of Proper and Unit Interval Graphs Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:39:30.669765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-14T11:39:30.123290Z digest=sha256:3a10d2259eacde6191221112cc90d399dfbb18babe19c0fa500dd0a6bcabbbd4

Pith citing papers

No inbound Pith citation observations are available.