Maximal cliques in {P2∪P3,C4}{P2∪P3,C4}-free graphs

We prove a decomposition theorem for the class GG of {P2∪P3,C4}{P2∪P3,C4}-free graphs. This theorem enables us to show that (i) every graph GG in GG has at most n+5n+5 maximal cliques where nn is the number of vertices in GG, and (ii) for every GG in GG, χ(G)≤⌈5ω(G)4⌉, where χ(G)χ(G) (ω(G)ω(G)) is the chromatic (clique) number of GG.