In graph theory, a maximally matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching in the graph.[1] An alternative term is allowed edge.[2][3]
A fundamental problem in matching theory is: given a graph G, find the set of all maximally matchable edges in G. This is equivalent to finding the union of all maximum matchings in G (this is different than the simpler problem of finding a single maximum matching in G). Several algorithms for this problem are known.
^Tassa, Tamir (2012-03-16). "Finding all maximally-matchable edges in a bipartite graph". Theoretical Computer Science. 423: 50–58. doi:10.1016/j.tcs.2011.12.071. ISSN 0304-3975.
^De Carvalho, Marcelo H.; Cheriyan, Joseph (2005-10-01). "An algorithm for ear decompositions of matching-covered graphs". ACM Transactions on Algorithms. 1 (2): 324–337. doi:10.1145/1103963.1103969. ISSN 1549-6325.
^Lovász, László; Plummer, Michael (2009-08-18). Matching Theory. Providence, Rhode Island: American Mathematical Society. doi:10.1090/chel/367. ISBN 9780821847596.
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