On the Chromatic Number of Some (P3 ∨ P2)-Free Graphs

Let G be a graph. We denote the chromatic (clique) number of G by chi(G)(omega(G)). In this paper, we prove that (i) chi(G) <= 2 omega(G) if G is (P-3 boolean OR P-2, kite)-free, (ii) chi(G) <= omega(2)(G) if G is (P-3 boolean OR P-2, hammer)-free, (iii) chi(G) <= 3 omega(2)(G)+omega(G)/2 if G is (P-3 boolean OR P-2, C-5)-free. Furthermore, we also discuss the chromatic number of (P-3 boolean OR P-2, K-4)-Free Graphs.

Automated summary

In this paper, we prove several results regarding the chromatic number of a graph and its relation to the freedom of specific graph structures, providing some restrictions for the chromatic number problem.