{"id":"palomar/PALOMAR-2026-10-28-000023","url":"https://github.com/jtraverso/thomassen-girth-five/tree/12765f3362b48fbae04ac467d33873a4f2234083","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000023-v1.json","repo":"https://github.com/jtraverso/thomassen-girth-five","tags":["math.CO","msc:05C15","msc:05C10"],"score":0,"title":"Thomassen: planar graphs of girth at least five are 3-choosable","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"3-List-Coloring Planar Graphs of Girth 5","identifier":"doi:10.1006/jctb.1995.1027","relationship":"formalizes"},{"title":"Choosability in signed planar graphs","identifier":"arxiv:1502.04561","relationship":"adapts"},{"title":"Graph Coloring Methods","identifier":"","relationship":"adapts"},{"title":"planar-list-colouring and grotzsch-ore registered Lean libraries","identifier":"","relationship":"adapts"},{"title":"Choosability of planar graphs of girth 5","identifier":"arxiv:1109.2976","relationship":"formalizes"}]}