On the Chromatic Number of Some (P3 ∪ P2)-Free Graphs
Rui Li, Jinfeng Li, Di Wu · Mathematics · 2023
Let G be a graph. We denote the chromatic (clique) number of G by χ(G)(ω(G)). In this paper, we prove that (i) χ(G)≤2ω(G) if G is (P3∪P2, kite)-free, (ii) χ(G)≤ω2(G) if G is (P3∪P2, hammer)-free, (iii) χ(G)≤3ω2(G)+ω(G)2 if G is (P3∪P2,C5)-free. Furthermore, we also discuss the chromatic number of (P3∪P2,K4)-Free Graphs.