{"id":"palomar/PALOMAR-2026-10-17-000009","url":"https://github.com/jtraverso/erdos-girth-chromatic/tree/05407c110b29ebb412667c688b2758d23bc744dd","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000009-v2.json","repo":"https://github.com/jtraverso/erdos-girth-chromatic","tags":["math.CO","msc:05C15","msc:05C38","msc:05C80","msc:05C72"],"score":0,"title":"Graphs of large girth and large chromatic number: Erdős, Mycielski, and the fractional chromatic number of Mycielski graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of three classical results on graphs with large chromatic number. (1) Erdős' 1959 theorem: for every g and k there is a finite graph with girth greater than g and chromatic number greater than k, in the structural form given by the probabilistic argument (for every ε > 0 and all large n, a graph on n vertices with girth greater than g whose independent sets have fewer than εn vertices). (2) Mycielski's 1955 construction M(G): it preserves and reflects triangle-freeness, M(G) is (k+1)-colourable exactly when G is k-colourable, χ(M(G)) = χ(G) + 1 for every…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Graph Theory and Probability","identifier":"doi:10.4153/CJM-1959-003-9","relationship":"formalizes"},{"title":"Sur le coloriage des graphs","identifier":"doi:10.4064/cm-3-2-161-162","relationship":"formalizes"},{"title":"The fractional chromatic number of Mycielski's graphs","identifier":"doi:10.1002/jgt.3190190313","relationship":"formalizes"}]}