Abstract Graph Factors and Matching Extensions deals with two important branches of graph
theory-factor theory and extendable graphs. Due to the mature techniques and wide ranges …

We consider the problem of finding all maximally-matchable edges in a bipartite graph G=(V,
E), ie, all edges that are included in some maximum matching. We show that given any …

This paper is concerned with structures of general graphs with perfect matchings. We first
reveal a partially ordered structure among elementary components of general graphs with …

Many real-life planning problems require making a priori decisions before all parameters of
the problem have been revealed. An important special case of such problem arises in …

The forcing number of a graph with a perfect matching $ M $ is the minimum number of
edges in $ M $ whose endpoints need to be deleted, such that the remaining graph only has …

Given a graph, a barrier is a set of vertices determined by the Berge formula—the min-max
theorem characterizing the size of maximum matchings. The notion of barriers plays …

Given a graph, a barrier is a set of vertices determined by the Berge formula---the min-max
theorem characterizing the size of maximum matchings. The notion of barriers plays …

Lovász shows that a matching covered graph G has an ear decomposition starting with an
arbitrary edge of G. A 2-edge-connected cubic graph is matching covered. Using Oum's …

A graph G with a perfect matching iscalled saturated ifC+ e has more perfect matchings than
a forany edge e that isnot in C. LovEsz gave a cliaracterization of the saturated graphs …

In matching theory, one of the most fundamental and classical branches of
combinatorics,{\em canonical decompositions} of graphs are powerful and versatile tools …