SEQUENCES, CLAWS AND CYCLABILITY OF GRAPHS

A subset S of vertices of a graph G is called cyclable in G if there i s in G some cycle containing ail the vertices of S. We give two result s on the cyclability of a vertex subset in graphs, one of which is rel ated to ''hamiltonian-nice-sequence'' conditions and the other of whic h is related to ''claw-free'' conditions; They imply many known result s on hamiltonian graph theory. Moreover, the analogous results related to the hamilton-connectivity or to the existence of dominating cycle are also given. (C) 1996 John Wiley & Sons, Inc.