A New Chvátal Type Condition For Pancyclicity

. Schmeichel and Hakimi [?], and Bauer and Schmeichel [?] gave an evidence in support of the well-known Bondy's "metaconjecture" that almost any non-trivial condition on graphs which implies that the graph is hamiltonian also implies that it is pancyclic. In particular, they proved that the metaconjecture is valid for Chv'atal's condition [?]. We slightly generalize their results giving a new Chv'atal type condition for pancyclicity. 1. Introduction Throughout, let G be a graph of order n 3. If G has a hamiltonian cycle (a cycle containing every vertex of G), then G is called hamiltonian. The graph G is said to be pancyclic if it contains cycles of every length l; 3 l n. By NG (u) (or simply N(u)) we denote the set of neighbours of u in G. We say that a set S ` V (G) is independent if there is no edge between vertices from S. The degree d(S) of the set S is defined as j [ v2S N(v) n Sj. Let dG (v) (or simply d(v)) denote the degree of the vertex v in a graph G. Finally, we define t..