It is welt-known that the largest cycles of a graph may have empty int
ersection. This is the case, for example, for any hypohamiltonian grap
h. In the literature, several important classes of graphs have been sh
own to contain examples with the above property. This paper investigat
es a (nontrivial) class of graphs which, on the contrary, admits no su
ch example. (C) 1997 John Wiley & Sons, Inc.