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Paper Citation Record · LEDGER

A note on two cycles of consecutive even lengths in graphs

As of 8 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2506.08692.

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

pith.paper-citation-record.v1
2506.08692 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:23:02.826989Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:49:03.558927Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:49:04.298924Z

Reference resolution

16 of 16 outbound references displayed

  • verified exact1
  • verified fuzzy8
  • unresolved7
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 143fdc79-c44c-474b-857e-f9a952fe4e61 · outbound

This paper cites Bollob´ as, Cycles modulok, Bull.

A note on two cycles of consecutive even lengths in graphs Bollob´ as, Cycles modulok, Bull

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:03.038258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.773118Z digest=sha256:35f30381b727a79c71a7f94f1825b061a5c6a28210dd9147bf556063c73c5a35

Observation 796d0db8-8bb6-43a2-b72a-1b668db29a21 · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:03.026644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.777169Z digest=sha256:fcf8b7d6bc342e09100bcd2f235afd3ac0c6c1880ef9039a5b0aa17070a582e6

Observation bbfcd193-7790-4b2f-b717-039ceca3acb2 · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:03.015565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.780571Z digest=sha256:7d503315604d028719bb4fc3c158bca74fac9b7ed8e513e96c577a7c4fc91a43

Observation 6a13313d-349e-406f-a795-09c37d705438 · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:03.004148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.784061Z digest=sha256:df7278e623b424f485dfcb4155f51331f2b3f3f98543b88aee068b7cb36ca984

Observation c90e4070-5dc0-4f45-9acd-1ed256042575 · outbound

This paper cites Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs.

A note on two cycles of consecutive even lengths in graphs Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-07T05:23:02.872214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.787618Z digest=sha256:e2a17cf3a0b0b540b3724247697273c2b3aed8894140f6276fa7037d54ddd1fa

Observation aef56583-8437-4170-b96a-8941b181c09a · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:02.992838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.791710Z digest=sha256:e8aa97bb8161e2c86aa5cbd32f6089245aae25e3f69a60ab1a3ea416391ef483

Observation 217ba930-f8c9-4fdd-ac84-b0ada2e4a04a · outbound

This paper cites Diwan, Cycles of even lengths modulok.

A note on two cycles of consecutive even lengths in graphs Diwan, Cycles of even lengths modulok

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.981178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.795588Z digest=sha256:2b5c07d76fafcb70579a7c02f2a34623aa80ed0814a2e38ef402f9ac89b771ba

Observation 627c7ecf-b637-4174-954c-5bf263a739b4 · outbound

This paper cites Fan, Distribution of cycle lengths in graphs, J.

A note on two cycles of consecutive even lengths in graphs Fan, Distribution of cycle lengths in graphs, J

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.970040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.798874Z digest=sha256:203704e10fac8cf5407a40bcc5021035d151dec22361ddaaecc9b96c88d86fb2

Observation 117658e0-cbf1-4165-97ad-2d66de946fcc · outbound

This paper cites F ¨uredi, D.S.

A note on two cycles of consecutive even lengths in graphs F ¨uredi, D.S

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.958631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.802562Z digest=sha256:2a697bd4cb324c40230b9b1c09d00cf21c5e48d06868d1204791d693274fd634

Observation ecaa83cf-65d3-4e4a-8662-fa7711bc6057 · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:02.946999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.806034Z digest=sha256:ab8401af0a9bbeb4cee061a3a624193ccec0258f18c30830e573e0edc6c1a1e8

Observation e85a7f43-49a4-4c1e-8827-61eecc6c0127 · outbound

This paper cites an unresolved cited work.

A note on two cycles of consecutive even lengths in graphs Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:23:02.934465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.809306Z digest=sha256:14660a3badb9fc87e2028ac7d3b7016441669ac3f2a013a6e1105fb5c5af45d4

Observation 8edfb1d3-cee4-4f4c-803f-af18a81c0795 · outbound

This paper cites On graphs without cycles of length 0 modulo 4.

A note on two cycles of consecutive even lengths in graphs On graphs without cycles of length 0 modulo 4

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-07T05:23:02.812754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T05:23:02.812754Z digest=sha256:67a91eeaeeec01c3c507ecfbdacb0c64631eb35ba9f96776d0c7a43c0343e839

Observation af0012f2-c71b-424f-9452-018b65821184 · outbound

This paper cites Sudakov, J.

A note on two cycles of consecutive even lengths in graphs Sudakov, J

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.921306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.816877Z digest=sha256:52a66bb8f7b468e9cd58e5dd877590e1036945037352424c885bdd1de940100a

Observation c2def4c7-ef29-4056-8be0-dc2b7fcc8f6e · outbound

This paper cites Thomassen, Cycles in graphs of uncountable chromatic number, Combinatorica 3 (1983) 133–134.

A note on two cycles of consecutive even lengths in graphs Thomassen, Cycles in graphs of uncountable chromatic number, Combinatorica 3 (1983) 133–134

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.909596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.820400Z digest=sha256:586cf1b134e72952847b5c61269e2b5bd3d864136b9b594bd1067e3ce80fa048

Observation f259beef-c683-403a-9d26-7a035ee5ace0 · outbound

This paper cites Thomassen, Paths, Circuits and Subdivisions in: Selected Topics in Graph Theory 3, L.

A note on two cycles of consecutive even lengths in graphs Thomassen, Paths, Circuits and Subdivisions in: Selected Topics in Graph Theory 3, L

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.897279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.823803Z digest=sha256:65c0ff8cb8b91b14283ee92b96a47583f33f2dda645b663b86614c4f0d761448

Observation 408cbb36-e0a6-4448-9735-6d693f73a98f · outbound

This paper cites Verstra ¨ete, Extremal problems for cycles in graphs, In Recent Trends Combinatorics, A.

A note on two cycles of consecutive even lengths in graphs Verstra ¨ete, Extremal problems for cycles in graphs, In Recent Trends Combinatorics, A

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:23:02.885029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T05:23:02.826989Z digest=sha256:8448e79bacd33391d4dca80392fa85852715ddb1164aff0e47dbedc17f999048

Pith citing papers

Observation 26250f58-353b-485b-8c4b-9bf6a2b177bf · inbound

On $2$-connected graphs avoiding cycles of length $0$ modulo $4$ cites this paper.

On $2$-connected graphs avoiding cycles of length $0$ modulo $4$ A note on two cycles of consecutive even lengths in graphs

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:49:04.412867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T16:49:03.558927Z digest=sha256:7c4f4439d367d88f656a1a42d47e4a2bdb32238ca14aa674bd06f8a2f0d0e7a7