An improvement of fraisse's sufficient condition for hamiltonian graphs

Abstract

AbstractLet G be a k‐connected graph of order n. For an independent set c, let d(S) be the number of vertices adjacent to at least one vertex of S and > let i(S) be the number of vertices adjacent to at least |S| vertices of S. We prove that if there exists some s, 1 ≤ s ≤ k, such that ΣxiEX d(X\{Xi}) > s(n−1) – k[s/2] – i(X)[(s−1)/2] holds for every independetn set X ={x0, x1 ⃛xs} of s + 1 vertices, then G is hamiltonian. Several known results, including Fraisse's sufficient condition for hamiltonian graphs, are dervied as corollaries.