HAMILTONICITY FOR K1,(R)-FREE GRAPHS

In this paper, we investigate the Hamiltonicity of K-1,K-r-free graphs with some degree conditions. In particular, let G be a k-connected gr aph of order n greater than or equal to 3 which is K-1,K-4-free. If Si gma(i=0)(k) d(upsilon(i)) greater than or equal to n + k for every ind ependent set {upsilon(0), upsilon(1), ..., upsilon(k)}, then G is hami ltonian. We use an upper bound for the independence number of K-1,K-r- free graphs to extend the above result to K-1,K-r-free graphs. Hamilto nian connected and, more generally, q-edge hamiltonian properties are studied here as well. (C) 1995 John Wiley & Sons, Inc.