Paper Citation Record · LEDGER

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2607.26271.

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

pith.paper-citation-record.v1
2607.26271 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T00:30:29.377408Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

31 of 31 outbound references displayed

verified exact11
verified fuzzy0
unresolved14
parse uncertain0
malformed identifier6
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d1fbee73-a909-44d6-9393-87f98d4f1158 · outbound

This paper cites On connectivity, conductance and bootstrap percolation for a random k-out, age-biased graph.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs On connectivity, conductance and bootstrap percolation for a random k-out, age-biased graph

Reference 1

Resolution: verified exact; doi, observed 2026-08-01T00:30:57.214491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e85bc71f-41df-4e93-be65-3fc4e6a7871e · outbound

This paper cites Coloring graphs with sparse neighborhoods.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Coloring graphs with sparse neighborhoods

Reference 2

Resolution: malformed identifier; no resolver link, observed 2026-08-01T00:30:26.403199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03162214-5faa-48cd-8547-0719d2e2320b · outbound

This paper cites Coloring graphs with forbidden bipartite sub- graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Coloring graphs with forbidden bipartite sub- graphs

Reference 3

Resolution: verified exact; doi, observed 2026-08-01T00:30:57.129291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7e419f0d-15e2-404a-bdd6-99c8fad4df6c · outbound

This paper cites The Johansson-Molloy theorem for DP-coloring.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs The Johansson-Molloy theorem for DP-coloring

Reference 4

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.965652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 038a32af-9eba-489d-a9ad-81230b5efa47 · outbound

This paper cites Counting colorings of triangle-free graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Counting colorings of triangle-free graphs

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-08-01T00:30:26.659572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59551f3d-24b4-4b26-950b-74813d3b13b0 · outbound

This paper cites Dynamic concentration of the triangle-free process.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Dynamic concentration of the triangle-free process

Reference 6

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.864429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1d20cf2d-caf1-46dd-b038-a85e5c8155ce · outbound

This paper cites Bradaˇ c, J.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Bradaˇ c, J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:26.796889Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78da1a6b-c977-4034-9d3e-d24c9fa6f4d5 · outbound

This paper cites Toward Vu's conjecture.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Toward Vu's conjecture

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:26.866426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98523e40-2a18-40fa-9964-1a7c121371c4 · outbound

This paper cites Campos, M.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Campos, M

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:26.903683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ba8d04e-623f-43e0-8c20-2402a03930aa · outbound

This paper cites Graph structure via local occupancy.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Graph structure via local occupancy

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.051185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 821ecb09-fae1-4668-b147-3725af3bf93e · outbound

This paper cites Fractional coloring via entropy.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Fractional coloring via entropy

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.111303Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae46fc08-d555-404f-aa9c-743914d61dcc · outbound

This paper cites Dhawan, O.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Dhawan, O

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.195735Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aa7101d0-8e13-4cd3-830c-2bc6026bf1f3 · outbound

This paper cites Separation choosability and dense bipartite induced subgraphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Separation choosability and dense bipartite induced subgraphs

Reference 13

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.720512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 662e5f0c-37c0-4bbe-b552-72bb26b941f8 · outbound

This paper cites The triangle-free process and the Ramsey number R(3, k).

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs The triangle-free process and the Ramsey number R(3, k)

Reference 14

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.569120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2e32554c-1b6d-4c21-ba97-8319facc772d · outbound

This paper cites Perfect matchings and Hamiltonian cycles in the preferential attachment model.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Perfect matchings and Hamiltonian cycles in the preferential attachment model

Reference 15

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.490514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 735435c4-874f-4080-a408-3ec509063f11 · outbound

This paper cites On the independence and chromatic numbers of random regular graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs On the independence and chromatic numbers of random regular graphs

Reference 16

Resolution: malformed identifier; no resolver link, observed 2026-08-01T00:30:27.580287Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 778ce0b7-a79c-4af6-a169-73c22bd87b19 · outbound

This paper cites Some results on chromatic number as a function of triangle count.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Some results on chromatic number as a function of triangle count

Reference 17

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.312888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 08285408-3729-4f48-a400-447115a9513e · outbound

This paper cites Hefty, P.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Hefty, P

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.758044Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62b0942d-0580-4279-a746-b491d1cd6dd5 · outbound

This paper cites Uniformly random colourings of sparse graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Uniformly random colourings of sparse graphs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.851536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54718058-09f8-4ada-ada1-4423734e14c0 · outbound

This paper cites Johansson.Asymptotic choice number for triangle free graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Johansson.Asymptotic choice number for triangle free graphs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:27.945309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80a5477c-e980-4c96-9b1d-cb0d3a17fe49 · outbound

This paper cites an unresolved cited work.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:28.060156Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b9f1fc8-3154-440a-806d-73461adb2c36 · outbound

This paper cites On Brooks’ theorem for sparse graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs On Brooks’ theorem for sparse graphs

Reference 22

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.160550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation afe76488-99d7-4b87-ad0f-9c8fde063fd9 · outbound

This paper cites γ-variable first-order logic of uniform attachment random graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs γ-variable first-order logic of uniform attachment random graphs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:28.389253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74005da2-0b6b-4367-808d-f7726d983d47 · outbound

This paper cites Random independent sets in triangle-free graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Random independent sets in triangle-free graphs

Reference 24

Resolution: malformed identifier; no resolver link, observed 2026-08-01T00:30:28.497804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8df59f38-2d25-493b-b68e-d527adc44eb1 · outbound

This paper cites Mitzenmacher and E.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Mitzenmacher and E

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:28.610295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95e7ea50-3b51-44aa-8c03-0bda743f0b5a · outbound

This paper cites The list chromatic number of graphs with small clique number.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs The list chromatic number of graphs with small clique number

Reference 26

Resolution: verified exact; doi, observed 2026-08-01T00:30:56.080314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 25a518b5-669f-4642-b527-b2bc0a49469d · outbound

This paper cites Molloy and B.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Molloy and B

Reference 27

Resolution: malformed identifier; no resolver link, observed 2026-08-01T00:30:28.906736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca1804f4-26f2-47ad-95bf-113bb87b1a6a · outbound

This paper cites The spectral density of Hardy kernel matrices.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs The spectral density of Hardy kernel matrices

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:29.083573Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea667817-d85c-4ca3-a5a6-e5387477c3d4 · outbound

This paper cites A note on the independence number of triangle-free graphs.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs A note on the independence number of triangle-free graphs

Reference 29

Resolution: malformed identifier; doi_truncated, observed 2026-08-01T00:30:55.843549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cdabec45-5a7a-44df-9266-998b348a7e11 · outbound

This paper cites an unresolved cited work.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs Unresolved cited work

Reference 30

Resolution: verified exact; doi, observed 2026-08-01T00:30:55.673305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bfc1164f-c9ee-43de-849d-405453be8264 · outbound

This paper cites A new lower bound for sphere packing.

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs A new lower bound for sphere packing

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-01T00:30:26.989506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.