Let G be a graph. We use χ(G) and ω(G) to denote the chromatic
number and clique number of G respectively. A P5 is a path on 5 vertices.
A family of graphs G is said to be {\itχ-bounded} if there
exists some function f such that χ(G)≤f(ω(G)) for every
G∈G. In this paper, we show that the family of (P5,K5−e)-free graphs is χ-bounded by a linear function: χ(G)≤max{13,ω(G)+1}.Comment: arXiv admin note: text overlap with arXiv:2204.0646