A Note on a Conjecture of Gyárfás

Ryan R.Martin1
1Department of Mathematics, lowa State University, Ames, IA 50011. The author partially supported by the Clay Mathematics Institute.

Abstract

This note proves that, given one member, \(T\), of a particular family of radius-three trees, every radius-two, triangle-free graph, \(G\), with large enough chromatic number contains an induced copy of \(T\).