ODD SUN-FREE TRIANGULATED GRAPHS ARE S-PERFECT

For a graph G with the vertex set V (G) and the edge set E(G) and a star subgraph S of G, let αS(G) be the maximum number of vertices in G such that no two of them are in the same star subgraph S and θS(G) be the minimum number of star sub-graph S that cover the vertices of G. A graph G is called S-perfect if for every induced subgraph H of G, αS(H) = θS(H). Motivated by perfect graphs discovered by Berge, Ravindra in-troduced S-perfect graphs. In this paper we prove that a trian-gulated graph is S-perfect if and only if G is odd sun-free. This result leads to a conjecture which if proved is a structural char-acterization of S-perfect graphs in terms of forbidden subgraphs.