{"id":"palomar/PALOMAR-2026-10-17-000009","url":"https://github.com/jtraverso/erdos-girth-chromatic/tree/e41d7493430ba42f18da380192a4111763155064","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000009-v1.json","repo":"https://github.com/jtraverso/erdos-girth-chromatic","tags":["math.CO","msc:05C15","msc:05C38","msc:05C80","graph-theory","large-girth","chromatic-number","lean-formalization"],"score":0,"title":"Erdős' theorem on graphs of large girth and large chromatic number","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of Erdős' 1959 theorem: for every g and k there is a finite graph with girth greater than g and chromatic number greater than k. The formalization proves the structural form given by Erdős' probabilistic argument: for every g and every ε > 0, for all sufficiently large n there is a graph on n vertices with no cycle of length at most g in which every independent set has fewer than εn vertices; hence, for all large n, a graph on n vertices with girth greater than g that is not k-colourable. Mathlib has girth and chromatic number but not this theorem;…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"Graph Theory and Probability","identifier":"doi:10.4153/CJM-1959-003-9","relationship":"formalizes"}]}