Open Research Index

Thomassen: planar graphs of girth at least five are 3-choosable

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-28-000023Oct 28, 2026math.COscore 0

Finite planar simple graphs of extended girth at least five are 3-choosable over arbitrary colour types. Includes a complete six-vertex boundary-extension induction, actual induced-face geometry and residual list-colouring infrastructure. Additional results expose the short-path theorem, derive an infinite finite-list compactness consequence, extend arbitrary five/six-cycles, and extend outer seven-cycles. The full original Theorem 2.1 and Corollary 2.2 are also proved, including arbitrary allowed fixed-edge colours and all exterior components.

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-28-000023
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-28-000023/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-28-000023/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'