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...

of the maximum weight matching problem is the assignment problem, in which the graph is a bipartite graph and the matching must have cardinality equal...

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...

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...

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...

is a perfect fractional matching with weights {1/2, 1/2, 1/2, 1/2, 1}. The problem of finding a maximum-cardinality matching in a hypergraph, thus calculating...

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...

included in at least one maximum-cardinality matching in the graph. An alternative term is allowed edge. A fundamental problem in matching theory is: given a...

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...

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

matching algorithms such as the Hopcroft–Karp algorithm for maximum cardinality matching work correctly only on bipartite inputs. As a simple example...

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...

maximum cardinality matching. Kőnig's theorem is equivalent to the following: The positivity graph of any bistochastic matrix admits a perfect matching. A...

matching (also called: maximum priority matching) is a matching that maximizes the number of high-priority vertices that participate in the matching....

matching of size n + r {\displaystyle n+r} . A minimum-cost perfect matching in this graph must consist of minimum-cost maximum-cardinality matchings...

to maintain full control of the network is determined by the maximum-cardinality matching in the network. From this result, an analytical framework, based...

of a set F of edges is the dot product 1E · 1F . Therefore, a maximum cardinality matching in G is given by the following integer linear program: Maximize...

graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, and...

cycle length, a maximum-cardinality and maximum-weight exchange can be found in polynomial time. For example, to find a maximum-cardinality exchange, given...

convert a bipartite graph to a maximum cardinality matching Hungarian algorithm: algorithm for finding a perfect matching Prüfer coding: conversion between...

Hopcroft–Karp algorithm, the fastest known method for finding maximum cardinality matchings in bipartite graphs. In 1980, along with Richard J. Lipton,...

equals its cardinality, and dependent if and only if it has greater cardinality than rank. A nonempty set is a circuit if its cardinality equals one plus...

+ 2 {\displaystyle n^{2}-2n+2} perfect matchings. A fractional matching of maximum cardinality (i.e., maximum sum of fractions) can be found by linear...

there exists a matching that saturates all the agents; this can be decided in polynomial time by just finding a maximum cardinality matching in the bipartite...

Processing Letters 74, 2000, 107-114. "The weighted matching approach to maximum cardinality matching," H.N. Gabow, Fundamenta Informaticae (Elegant Structures...

proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs. It...

Alt, H.; Blum, N.; Mehlhorn, K.; Paul, M. (1991), "Computing a maximum cardinality matching in a bipartite graph in time O ( n 1.5 m / log ⁡ n ) {\textstyle...

there is an algorithm that runs in time f (OPT)nO(1) where OPT is the cardinality of the smallest hitting set. The hitting set problem is fixed-parameter...

speaking, maximum consensus solves the following optimization: where | I | {\displaystyle \vert {\mathcal {I}}\vert } denotes the cardinality of the set...