On paw path convexity in graphs

A triangle path T between two non-adjacent vertices in a graph G is called pt-path if one and only vertex of T, the first vertex or the last, can be on a chord. In the resulting interval convexity, a set S of vertices of G is a pt-convex if for any two non-adjacent vertices u, v of S any vertex in a pt-path between u and v is also in S. The main result of the paper is that a graph is a convex geometry with respect to pt-convexity if and only if it is a chordal graph paw free. Furthermore, some invariants are studied with respect to pt-convexity.