Chromatic Ramsey numbers of generalised Mycielski graphs

Abstract

. We revisit the Burr–Erd˝os–Lov´asz conjecture on chromatic Ramsey numbers. We show that it admits a proof based on the Lov´asz ϑ parame- ter in addition to the proof of Xuding Zhu based on the fractional chromatic number. However, there are no proofs based on topological lower bounds on chromatic numbers, because the chromatic Ramsey numbers of generalised Mycielski graphs are too large. We show that the 4-chromatic generalised Mycielski graphs other than K 4 all have chromatic Ramsey number 14, and that the n -chromatic generalised Mycielski graphs all have chromatic Ramsey number at least 2 n/ 4 .