Erdős' theorem on graphs of large girth and large chromatic number
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;…
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