On the chromatic number of (P5, K2,t)-free graphs

In this paper we study the chromatic number of (P5, K2,t)-free graphs with t≥2. It is still an open question whether there are polynomial (χ-binding) functions fk for k≥5 such that every Pk-free graph G satisfies χ(G)≤fk(ω(G)), where Pk is an induced path on k vertices. Our main result is that every (P5, K2,t)-free graph G admits a polynomial χ-binding function. Moreover, we will present polynomial χ-binding functions for several other subclasses of P5-free graphs.