{"id":"palomar/PALOMAR-2026-11-01-000024","url":"https://github.com/jtraverso/borodin-light-triangles/tree/5a2639b3fc7d14491f1c79de46fa49cb38c64ddf","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-01-000024-v2.json","repo":"https://github.com/jtraverso/borodin-light-triangles","tags":["math.CO","msc:05C10","msc:05C07"],"score":0,"title":"Borodin's light triangles in planar graphs of minimum degree five","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of Borodin's theorem on light triangles, for finite simple graphs with the combinatorial planarity (genus-zero rotation systems) of the registered entry Kuratowski's theorem. The weight of a triangle is the sum of the degrees of its vertices. Every plane map of a graph of minimum degree at least five has a face of length three of weight at most 17 (light_face), and hence a planar graph of minimum degree at least five has a triangle of weight at most 17 (light_triangle). Two statements. The proof is a discharging argument run on the rotation system, with face…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-01","reactions":{},"formalized":true,"formalizes":[{"title":"Solution of problems of Kotzig and Grünbaum concerning the isolation of cycles in planar graphs","identifier":"doi:10.1007/BF01139613","relationship":"formalizes"},{"title":"An introduction to the discharging method via graph coloring","identifier":"arXiv:1306.4434","relationship":"formalizes"}]}