Maximal cliques in -free graphs

We prove a decomposition theorem for the class G of { P 2 ∪ P 3 , C 4 } -free graphs. This theorem enables us to show that (i) every graph G in G has at most n + 5 maximal cliques where n is the number of vertices in G , and (ii) for every G in G , χ ( G ) ≤ ⌈ 5 ω ( G ) 4 ⌉ , where χ ( G ) ( ω ( G ) ) is the chromatic (clique) number of G .