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Any regular bipartite graph. [1] Hall's marriage theorem can be used to show that a k-regular bipartite graph contains a perfect matching. One can then remove the perfect matching to obtain a (k − 1)-regular bipartite graph, and apply the same reasoning repeatedly. Any complete graph with an even number of nodes (see below). [2]
Kőnig had announced in 1914 and published in 1916 the results that every regular bipartite graph has a perfect matching, [11] and more generally that the chromatic index of any bipartite graph (that is, the minimum number of matchings into which it can be partitioned) equals its maximum degree [12] – the latter statement is known as Kőnig's ...
Let G be a bipartite graph, M a maximum-cardinality matching in G, and V 0 the set of vertices of G unmatched by M (the "free vertices"). Then G can be partitioned into three parts: The E-O-U decomposition. E - the even vertices - the vertices reachable from V 0 by an M-alternating path of even length.
In the other direction, from any bipartite graph = (,,) one can define a finite family of sets, the family of neighborhoods of the vertices in , such that any system of unique representatives for this family corresponds to an -perfect matching in . In this way, the combinatorial formulation for finite families of finite sets and the graph ...
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Cash App customers may be able to claim more than $2,500 each as part of a $15 million class-action settlement for data and security breaches at the mobile payment service.
Verizon settlement payments have started hitting customers' bank accounts as part of a $100 million resolution of a class-action lawsuit.. Eligible customers had until April 15 to claim their ...
Police believe Herb Baumeister targeted gay men and buried at least 25 victims on $1 million Indiana estate in the 1990s
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