Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph G, and the goal is to find a matching containing as many edges...

examples of maximal matchings (red) in three graphs. A maximum matching (also known as maximum-cardinality matching) is a matching that contains the largest...

the matching constrained to be have cardinality that of the smaller of the two partitions. Another special case is the problem of finding a maximum cardinality...

literature, the term complete matching is used. Every perfect matching is a maximum-cardinality matching, but the opposite is not true. For example, consider the...

the maximum flow in N {\displaystyle N} is equal to the size of the maximum matching in G {\displaystyle G} , and a maximum cardinality matching can be...

algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible with the property...

maximum cardinality matching in G that has minimum cost. Let w: E → R be a weight function on the edges of E. The minimum weight bipartite matching problem...

maximum-cardinality matching, but does not depend on which matching is chosen (the decomposition is the same for every maximum-cardinality matching chosen)...

is a maximum-cardinality matching. The sets E, O, U do not depend on the maximum-cardinality matching M (i.e., any maximum-cardinality matching defines...

is trivial. When k=2, the problem is equivalent to finding a maximum cardinality matching, which can be solved in polynomial time. For any k≥3, the problem...