STRONGLY HAMILTONIAN-CONNECTED LOCALLY SEMICOMPLETE DIGRAPHS

We give some sufficient conditions for locally semicomplete digraphs t o contain a hamiltonian path from a prescribed vertex to another presc ribed vertex. As an immediate consequence of these, we obtain that eve ry 4-connected locally semicomplete digraph is strongly hamiltonian-co nnected. Our results extend those of Thomassen [12] for tournaments. ( C) 1996 John Wiley & Sons, Inc.