{"id":"palomar/PALOMAR-2026-11-02-000013","url":"https://github.com/jtraverso/fabrici-jendrol-light-paths/tree/00ea06f84dc1b2b33d58a2b17361fc3a58189814","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-02-000013-v1.json","repo":"https://github.com/jtraverso/fabrici-jendrol-light-paths","tags":["math.CO","msc:05C10","msc:05C38","msc:05C07"],"score":0,"title":"Light paths and only paths in 3-connected planar graphs (Fabrici–Jendrol')","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of the two theorems of Fabrici and Jendrol' (1997), for finite simple graphs with the combinatorial planarity (genus-zero rotation systems) of the registered entry Kuratowski's theorem. Theorem 1 (light_path): a 3-connected planar graph that contains a path on k ≥ 1 vertices contains such a path whose vertices all have degree at most 5k. Theorem 2 (only_paths_light): for every connected planar graph H that is not a path (not isomorphic to pathGraph on its vertex count) and every m, there is a 3-connected planar graph containing a copy of H in which every copy…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-02","reactions":{},"formalized":true,"formalizes":[{"title":"Subgraphs with restricted degrees of their vertices in planar 3-connected graphs","identifier":"doi:10.1007/BF03353001","relationship":"formalizes"}]}