Edge proximity conditions for extendability in cubic bipartite graphs

We show that a set M of m edges in a cyclically (3 m  − 2)‐edge‐connected cubic bipartite graph is contained in a 1‐factor whenever the edges in M are pairwise distance at least f ( m ) apart, where$$f\left( m \right) = \left\{ {\matrix{{1,} \hfill & {m = 2} \hfill \cr {3,} \hfill & {3 \le m \le 4} \hfill \cr {4,} \hfill & {5 \le m \le 8} \hfill \cr {5,} \hfill & {m \ge 9.} \hfill \cr } } \right.$$ © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 112–120, 2007