Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:33:37.876527Z
Paper Citation Record · LEDGER
Every graph with no $K_7^{\vee}$-minor is $6$-colorable
As of 14 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2507.03244.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
21 of 21 outbound references displayed
- verified exact3
- verified fuzzy14
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1f182f1b-e580-429e-beea-fdcbe01ed1c8 · outbound
This paper cites On triangles in K_r -minor free graphs.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable On triangles in K_r -minor free graphs
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:42.409693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1f8de84d-5bb1-4b66-8f44-31aed7451b28 · outbound
This paper cites Appel and W.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Appel and W
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:42.250500Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 68cd6bdb-44e1-430a-b12a-d9ef8a80067b · outbound
This paper cites Appel, W.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Appel, W
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:42.061619Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 047679b1-3ffd-4de0-a9f4-892af7c4b862 · outbound
This paper cites an unresolved cited work.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:33:41.920035Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c5ef8045-f6b0-47cd-90fb-ef8526f1340d · outbound
This paper cites an unresolved cited work.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:33:41.748395Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 17252c17-58c8-4d90-bb3f-4fc3a7612891 · outbound
This paper cites Hadwiger.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Hadwiger
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:41.576635Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3d3f2c5c-0518-4fe6-ab03-a2a0406744f8 · outbound
This paper cites an unresolved cited work.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:33:41.445604Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 237afa57-5adc-4e22-b683-c2a3d38ef01b · outbound
This paper cites J rgensen.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable J rgensen
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:41.286302Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d6139a41-ad96-42c1-90fd-9767a9d28e2e · outbound
This paper cites On the structure of k -connected graphs without K _k -minor.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable On the structure of k -connected graphs without K _k -minor
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:41.091833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d35a7e91-7f7f-452d-8730-df281daaf4cd · outbound
This paper cites Kempe Chains and Rooted Minors.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Kempe Chains and Rooted Minors
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:33:38.493355Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f2b4eff1-4f51-4fa1-9c07-5a2a270027cd · outbound
This paper cites Any 7-chromatic graph has K _7 or K _ 4,4 as a minor.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Any 7-chromatic graph has K _7 or K _ 4,4 as a minor
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:40.796370Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation bdda858b-9b92-4fe3-80d3-fa7c13bdb028 · outbound
This paper cites Every graph with no $\mathcal{K}_8^{-4}$ minor is $7$-colorable.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Every graph with no $\mathcal{K}_8^{-4}$ minor is $7$-colorable
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:33:38.268790Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3e1da162-f585-49aa-a6e8-2de28b5c8847 · outbound
This paper cites Every graph with no $\mathcal{K}_9^{-6}$ minor is $8$-colorable.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Every graph with no $\mathcal{K}_9^{-6}$ minor is $8$-colorable
Reference 13
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:33:38.038415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 820dbb6d-1db6-4bdf-9deb-eaf156ac4368 · outbound
This paper cites an unresolved cited work.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:33:40.440540Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f5d27037-7796-4e58-85b0-dcdce97bb58e · outbound
This paper cites Graphs with no K_9^= -minor are 10 -colorable.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Graphs with no K_9^= -minor are 10 -colorable
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:40.054181Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c6c7d663-4c19-40c9-b98e-5b0039524406 · outbound
This paper cites Coloring graphs with forbidden minors.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Coloring graphs with forbidden minors
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:39.890258Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 052e337f-a4cb-4f21-a685-59502abfa569 · outbound
This paper cites Hadwiger's conjecture for K _6 -free graphs.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Hadwiger's conjecture for K _6 -free graphs
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:39.677577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation dbd107be-9dc3-4818-ae5b-5d8b34f3206f · outbound
This paper cites Properties of 8 -contraction-critical graphs with no K_7 minor.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Properties of 8 -contraction-critical graphs with no K_7 minor
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:39.389361Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e52a25fa-d0ac-43ad-97cf-64704662c16b · outbound
This paper cites Hadwiger s conjecture , pages 417--437.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Hadwiger s conjecture , pages 417--437
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:39.151103Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation dad17434-5fda-4a9d-883e-4f7bc209f781 · outbound
This paper cites \"U ber eine E igenschaft der ebenen K omplexe.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable \"U ber eine E igenschaft der ebenen K omplexe
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:38.900576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1fc907ad-5c42-4c3b-af15-073c6ca4a677 · outbound
This paper cites Extremal functions for rooted minors.
Every graph with no $K_7^{\vee}$-minor is $6$-colorable Extremal functions for rooted minors
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:33:38.690272Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.