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Matching polynomial. In the mathematical fields of graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. It is one of several graph polynomials studied in algebraic graph theory.
Matching (graph theory) In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. [1] In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated ...
Stable marriage problem. In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of ...
t. e. In economics, search and matching theory is a mathematical framework attempting to describe the formation of mutually beneficial relationships over time. It is closely related to stable matching theory. Search and matching theory has been especially influential in labor economics, where it has been used to describe the formation of new jobs.
Blossom algorithm. In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and |M ...
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G = (V, E), a perfect matching in G is a subset M of edge set E, such that every vertex in the vertex set V is adjacent to exactly one edge in M. A perfect matching is also called a 1-factor; see Graph factorization ...
Conversely, Kőnig's theorem proves the perfection of the complements of bipartite graphs, a result proven in a more explicit form by Gallai (1958). One can also connect Kőnig's line coloring theorem to a different class of perfect graphs, the line graphs of bipartite graphs. If G is a graph, the line graph L (G) has a vertex for each edge of ...
Induced matching. In graph theory, an induced matching or strong matching is a subset of the edges of an undirected graph that do not share any vertices (it is a matching) and these are the only edges connecting any two vertices which are endpoints of the matching edges (it is an induced subgraph). An induced matching can also be described as ...