Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes - Chudnovsky, M; Scott, A; Seymour, P; Spirkl, S (Elsevier, 2019)
We prove a conjecture of András Gyárfás, that for all k, ℓ, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least ℓ.