Abstract
AbstractLet be a matching‐covered graph and be an edge set of . is said to be feasible if there exist two perfect matchings and in such that . For any is said to be switching‐equivalent to , where is the set of edges in each of which has exactly one end in and is the symmetric difference of two sets and . Lukot'ka and Rollová showed that when is regular and bipartite, is nonfeasible if and only if is switching‐equivalent to . This article extends Lukot'ka and Rollová's result by showing that this conclusion holds as long as is matching‐covered and bipartite. This article also studies matching‐covered graphs whose nonfeasible edge sets are switching‐equivalent to or and partially characterizes these matching‐covered graphs in terms of their ear decompositions. Another aim of this article is to construct infinite many ‐connected and ‐regular graphs of class 1 containing nonfeasible edge sets not switching‐equivalent to either or for an arbitrary integer with , which provides a negative answer to a problem proposed by He et al.
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