International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 103-106
doi:10.1155/S0161171298000131
Longest cycles in certain bipartite graphs
Department of Mathematics and Computer Science, Seton Hall University, South Orange 07079, NJ, USA
Received 10 July 1995; Revised 25 October 1995
Copyright © 1998 Pak-Ken Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let G be a connected bipartite graph with bipartition (X,Y) such that |X|≥|Y|(≥2),
n=|X| and m=|Y|. Suppose, for all vertices x∈X and y∈Y, dist(x,y)=3 implies
d(x)+d(y)≥n+1. Then G contains a cycle of length 2m. In particular, if m=n, then G is
hamiltomian.