It is shown that there are two positive constants c1, c2 such that the maximum possible chromatic number of a triangle-free graph with m > 1 edges is at most c1m1/3/(log m)2/3 and at least c2m1/3/(log m)2/3. This is deduced from results of Ajtai, Komlós, Szemerédi, Kim and Johansson, and settles a problem of Erdös. © 2000 Elsevier Science B.V. All rights reserved.
Nilli, A. (2000). Triangle-free graphs with large chromatic numbers. Discrete Mathematics, 211(1–3), 261–262. https://doi.org/10.1016/S0012-365X(99)00109-0