Sequences,claws and cyclability of graphs

A subset S of vertices of a graph G is called cyclable in G if there is in G some cycle containing all the vertices of S. We give two results on the cyclability of a vertex subset in graphs, one of which is related to “hamiltonian-nice-sequence” conditions and the other of which is related to “claw-free” conditions. They imply many known results on hamiltonian graph theory. Moreover, the analogous results related to the hamilton-connectivity or to the existence of dominating cycle are also given. © 1996 John Wiley & Sons, Inc.