International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 103-106

Longest cycles in certain bipartite graphs

Pak-Ken Wong

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.


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 xX and yY, 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.