Hamiltonicity for K1, r-free graphs

In this paper, we investigate the Hamiltonicity of K_1,r-free graphs with some degree conditions. In particular, let G be a k-connected grph of order n≧3 which is K_1,4-free. If for every independent set {v₀, v₁, …, v_k} then G is hamiltonian. We use an upper bound for the independence number of K_1,r-free graphs to extent the above result to K_1,r-free graphs. Hamiltonian connected and, more generally, q-edge hamiltonian properties are studied here as well. © 1995 John Wiley & Sons, Inc.