An improvement of fraisse's sufficient condition for hamiltonian graphs

Let G be a k-connected graph of order n. For an independent set S c V, let d(S) be the number of vertices adjacent to a t least one vertex of Sand (if IS( 2 2) let i(S) be the number of vertices adjacent to at least IS1 1 vertices of S. We prove that if there exists some s, 1 I s I k, such that z,EX d(fl{x;}) > s(n 1) qs/21 i(X)L(s 1)/21 holds for every… CONTINUE READING