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

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