Paper Citation Record · LEDGER

Triangle-free $d$-degenerate graphs have small fractional chromatic number

As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2501.18238.

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

pith.paper-citation-record.v1
2501.18238 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T00:24:26.488885Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

27 of 27 outbound references displayed

verified exact4
verified fuzzy13
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a6e8084a-460a-4c93-b578-326b17f3a9d5 · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:29.609868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation be7fcd34-c9d9-4bb2-af89-10065ea1aca1 · outbound

This paper cites Anderson, A.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Anderson, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.541993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4c1bcfb1-2c66-471a-975c-24c8ea113d88 · outbound

This paper cites Anderson, A.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Anderson, A

Reference 3

Resolution: verified exact; raw_fallback, observed 2026-08-10T00:24:26.824994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9d0793e5-0fdb-4a7d-bc80-370e010fd635 · outbound

This paper cites Bollob´ as: The independence ratio of regular graphs, Proc.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Bollob´ as: The independence ratio of regular graphs, Proc

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.485244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 027d4eab-bda7-4790-8227-7c2c48bccdaf · outbound

This paper cites Bonamy, T.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Bonamy, T

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.455367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 93d2929d-a502-4968-9cb2-c52ffda8ac99 · outbound

This paper cites Bipartite graphs are $(\frac{4}{5}-\varepsilon) \frac{\Delta}{\log \Delta}$-choosable.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Bipartite graphs are $(\frac{4}{5}-\varepsilon) \frac{\Delta}{\log \Delta}$-choosable

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T00:24:26.365185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41d1a285-1d4b-4aed-8680-fc2f3e8c6c00 · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:29.436378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2d196b3c-3c4c-47d9-8ffa-710135f58a30 · outbound

This paper cites Davies, M.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Davies, M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.416517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7a57d31f-8f32-4f38-a738-f34508edda0b · outbound

This paper cites Davies, R.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Davies, R

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.393946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2674f12a-3afd-49db-a875-e902c7253236 · outbound

This paper cites Graph structure via local occupancy.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Graph structure via local occupancy

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T00:24:26.388732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3d56832-3736-4667-8008-c750859ab9aa · outbound

This paper cites The hard-core model in graph theory.

Triangle-free $d$-degenerate graphs have small fractional chromatic number The hard-core model in graph theory

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T00:24:26.395251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 734487f6-46af-4bf2-aa40-e8db209839c8 · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:29.371453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e64ecb97-a2fe-4b46-84ce-a9a268a5e5ea · outbound

This paper cites Esperet, R.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Esperet, R

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.350911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5848da67-bdf6-47d1-bf64-a3359e1f2713 · outbound

This paper cites Harris: Some results on chromatic number as a funct ion of triangle count, SIAM Journal on Discrete Mathematics 33(1), 2019, 546-–563.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Harris: Some results on chromatic number as a funct ion of triangle count, SIAM Journal on Discrete Mathematics 33(1), 2019, 546-–563

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:29.331105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 17e11b38-d45b-44dc-84b7-1c4c16c9889b · outbound

This paper cites Hurley, R.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Hurley, R

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:27.001588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3e02130f-7748-41ec-884b-1c738c21eda4 · outbound

This paper cites Colouring locally sparse graphs with the first moment method.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Colouring locally sparse graphs with the first moment method

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T00:24:26.646292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f240f29c-d4c2-4041-a783-9c8d0839c170 · outbound

This paper cites Hurley, F.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Hurley, F

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:26.981653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 31b45302-cb66-4300-8a0e-fcfc24bfe847 · outbound

This paper cites Chromatic number and regular subgraphs.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Chromatic number and regular subgraphs

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-10T00:24:26.614422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2618f161-20cf-4686-9a9a-5f888d57acf8 · outbound

This paper cites Johansson: Asymptotic choice number for triangle fr ee graphs.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Johansson: Asymptotic choice number for triangle fr ee graphs

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:26.962870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0430db5e-3eab-4ff1-95a7-d6d39d4788b4 · outbound

This paper cites Kelly, L.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Kelly, L

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:26.943036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3fb9eeb8-4724-49c4-ad44-93fc6ed7d322 · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:26.923751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6ce05556-1d0f-4c03-8c1b-40cef181f3eb · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:26.902849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 09c4e3d7-7386-4932-b816-bbb719f95efc · outbound

This paper cites A simplified proof of the Johansson-Molloy Theorem using the Rosenfeld counting method.

Triangle-free $d$-degenerate graphs have small fractional chromatic number A simplified proof of the Johansson-Molloy Theorem using the Rosenfeld counting method

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T00:24:26.464890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56f8c476-82b7-4d39-a404-c00f6888038a · outbound

This paper cites Local Shearer bound.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Local Shearer bound

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-10T00:24:26.548204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f38d4e03-b3fd-4758-950a-c47972774137 · outbound

This paper cites Molloy: The list chromatic number of graphs with smal l clique number.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Molloy: The list chromatic number of graphs with smal l clique number

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:26.883019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4e002f2a-9a9a-427f-8af8-9420418ffc3f · outbound

This paper cites Pirot and J.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Pirot and J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T00:24:26.863511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2d027497-ec02-4ca1-87ce-49521fe2cac9 · outbound

This paper cites an unresolved cited work.

Triangle-free $d$-degenerate graphs have small fractional chromatic number Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-10T00:24:26.844957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.