On the chromatic number of (P_{5},windmill)-free graphs
Ingo Schiermeyer · Opuscula Mathematica · 2017
In this paper we study the chromatic number of (P5, windmill)-free graphs.For integers r, p ≥ 2 the windmill graph W p r+1 = K1 ∨pKr is the graph obtained by joining a single vertex (the center) to the vertices of p disjoint copies of a complete graph Kr.Our main result is that every (P5, windmill)-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.