GRAPHS WITH EVERY PATH OF LENGTH k IN A HAMILTONIAN CYCLE

In this paper we prove that if G is a (k + 2)-connected graph on n > 3 vertices satisfying P(n + k) : dG(x; y) = 2 ) maxfd(x); d(y)g > n + k 2 for each pair of vertices x and y in G; then any path S G of length k is contained in a hamiltonian cycle of G