Affiliation:
1. Department of Mathematics and Statistics University of Otago Dunedin New Zealand
2. School of Mathematical Sciences, Queen Mary University of London London England
3. Department of Mathematics Vanderbilt University Nashville Tennessee USA
Abstract
AbstractLet and be positive integers with , let be an ‐regular cyclically ‐edge‐connected bipartite graph and let be a matching of size in . Plummer showed that whenever , there is a perfect matching of containing . When , Aldred and Jackson, extended this result to the case when by showing there is a perfect matching in containing whenever the edges in are pairwise at least distance apart where
In this paper, we relax the condition that and the distance restriction introduced by Aldred and Jackson to show that, for and an ‐regular cyclically ‐edge‐connected bipartite graph, for each matching in with and such that each pair of edges in is distance at least 3 apart, there is a perfect matching in containing .
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics