Coloring of (P5, 4-wheel)-free graphs

Abstract

For a graph G, χ(G)(ω(G)) denote its chromatic (clique) number. A P5 is the chordless path on five vertices, and a 4-wheel is the graph consisting of a chordless cycle on four vertices C4 plus an additional vertex adjacent to all the vertices of the C4. In this paper, we show that every (P5, 4-wheel)-free graph G satisfies χ(G)≤32ω(G). Moreover, this bound is almost tight. That is, there is a class of (P5, 4-wheel)-free graphs L such that every graph H∈L satisfies χ(H)≥107ω(H). This generalizes/improves several previously known results in the literature.