Cycles through a prescribed vertex set in N-connected graphs

AbstractA well-known result of Dirac (Math. Nachr. 22 (1960) 61) says that given n vertices in an n-connected G, G has a cycle through all of them. In this paper, we generalize Dirac's result as follows:Given at most 32n vertices in an n-connected graph G when n⩾3 and |V(G)|⩾32n, then G has a cycle through exactly n vertices of them.This improves the previous known bound given by Kaneko and Saito (J. Graph Theory 15(6) (1991) 655)