New bounds on the generalized Ramsey number f(n,5,8)

Abstract

Let f(n,p,q) denote the minimum number of colors needed to color the edges of Kn so that every copy of Kp receives at least q distinct colors. In this note, we show 67(n−1)≤f(n,5,8)≤n+o(n). The upper bound is proven using the “conflict-free hypergraph matchings method” which was recently used by Mubayi and Joos to prove f(n,4,5)=56n+o(n).