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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 103-106
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 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.