Paper Citation Record · LEDGER

Progress towards Nash-Williams' Conjecture on Triangle Decompositions

As of 15 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:1909.00514.

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

pith.paper-citation-record.v1
1909.00514 v3

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T05:56:05.780420Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:30:55.419496Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T10:30:55.482225Z

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy16
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 676d8132-e7d1-42c0-a187-2d2132762af0 · outbound

This paper cites Barber, D.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Barber, D

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.072325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 43d4d8a5-6665-4219-a99f-1c6731c778e8 · outbound

This paper cites Barber, D.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Barber, D

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.058401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 178acbf1-642d-4154-ae53-52910f9943eb · outbound

This paper cites Barber, S.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Barber, S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.044010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6584bd3c-93d1-417a-8f87-4bc65ed7f82c · outbound

This paper cites Condon, J.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Condon, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.029873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 021145ba-b791-484e-afdf-c7ea3a397ddc · outbound

This paper cites Dross, Fractional triangle decompositions in graphs with large minimum degree, SIAM Journal on Discrete Mathematics , 30(1), 2015, 36–42.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Dross, Fractional triangle decompositions in graphs with large minimum degree, SIAM Journal on Discrete Mathematics , 30(1), 2015, 36–42

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.016373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 70aa4009-2249-4c59-bae0-f422d7370ee6 · outbound

This paper cites Dukes, Rational decomposition of dense hypergraphs and so me related eigenvalue estimates, Linear Algebra and Its Applications , 436(9), 2012, 3736–3746.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Dukes, Rational decomposition of dense hypergraphs and so me related eigenvalue estimates, Linear Algebra and Its Applications , 436(9), 2012, 3736–3746

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:06.001830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 65092759-a2f5-46dc-b2b7-f93ca0ec85c9 · outbound

This paper cites Dukes and D.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Dukes and D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.987156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a4648f5c-b812-4c62-904f-9cfd9acfa742 · outbound

This paper cites Garaschuk.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Garaschuk

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.972110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8939c050-2577-45f8-9b4e-dc2bc84d1e34 · outbound

This paper cites Glock, D.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Glock, D

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.957182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cf134843-29f0-4751-8d65-b3fe3cee19bf · outbound

This paper cites The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T05:56:05.743677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c71d2922-2c50-40ea-8445-3b902090ccf4 · outbound

This paper cites Glock, D.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Glock, D

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.942856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cad1608f-7589-45fa-9f99-4b0abbe3aae9 · outbound

This paper cites Haxell and V.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Haxell and V

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.927167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 546d46df-9cff-4c03-8559-1363c09e6c82 · outbound

This paper cites The existence of designs.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions The existence of designs

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T05:56:05.757429Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 179bf33e-128d-412f-8208-92409ffd718b · outbound

This paper cites Kirkman, On a problem in combinatorics, Cambridge Dublin Mathematical Jour- nal, 2, 1847, 191–204.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Kirkman, On a problem in combinatorics, Cambridge Dublin Mathematical Jour- nal, 2, 1847, 191–204

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.910508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 76e89eb9-2cfc-4f3f-ae63-b01dd6353a43 · outbound

This paper cites Montgomery, Fractional Clique Decompositions of Dense Gra phs, Random Structures and Algorithms , 54(4), 2019, 779–796.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Montgomery, Fractional Clique Decompositions of Dense Gra phs, Random Structures and Algorithms , 54(4), 2019, 779–796

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.895086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation be50c6d3-f612-44fc-9d6f-85c961bfd5f5 · outbound

This paper cites Nash-Williams, An unsolved problem concerning decompositio n of graphs into triangles, Combinatorial Theory and its Applications , III, 1970, 1179–1183.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Nash-Williams, An unsolved problem concerning decompositio n of graphs into triangles, Combinatorial Theory and its Applications , III, 1970, 1179–1183

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.879065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 18d91615-7de7-4f4c-b974-61704661b4e9 · outbound

This paper cites Wilson, Decomposition of complete graphs into subgraphs iso morphic to a given graph, Congressus Numerantium XV , 1975, 647–659.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Wilson, Decomposition of complete graphs into subgraphs iso morphic to a given graph, Congressus Numerantium XV , 1975, 647–659

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.863245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d1c8ed6b-4897-4476-a1fd-ee8fa2a70080 · outbound

This paper cites Yuster, Asymptotically optimal Kk-packings of dense graphs via fractional Kk- decompositions, Journal of Combinatorial Theory Series B , 95, 2005, 1–11.

Progress towards Nash-Williams' Conjecture on Triangle Decompositions Yuster, Asymptotically optimal Kk-packings of dense graphs via fractional Kk- decompositions, Journal of Combinatorial Theory Series B , 95, 2005, 1–11

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:56:05.847402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation c4a400e9-7bf6-4f70-875a-4cc1cc844d93 · inbound

On the minimum degree required for a triangle decomposition cites this paper.

On the minimum degree required for a triangle decomposition Progress towards Nash-Williams' Conjecture on Triangle Decompositions

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:30:55.489057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.