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Journal of the Franklin Institute, 1987
A general formula is derived for the matching polynomial of an arbitrary graph G. This yields a method for counting matchings in graphs. From the general formula, explicit formulae are deduced for the number of k- matchings in several well-known families of graphs.
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A general formula is derived for the matching polynomial of an arbitrary graph G. This yields a method for counting matchings in graphs. From the general formula, explicit formulae are deduced for the number of k- matchings in several well-known families of graphs.
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Canadian Journal of Mathematics, 1977
Tutte [9] has given necessary and sufficient conditions for a finite graph to have a perfect matching. Different proofs are given by Brualdi [1] and Gallai [2; 3]. The shortest proof of Tutte's theorem is due to Lovasz [5]. In another paper [10] Tutte extended his conditions for a perfect matching to locally finite graphs.
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Tutte [9] has given necessary and sufficient conditions for a finite graph to have a perfect matching. Different proofs are given by Brualdi [1] and Gallai [2; 3]. The shortest proof of Tutte's theorem is due to Lovasz [5]. In another paper [10] Tutte extended his conditions for a perfect matching to locally finite graphs.
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Matchings in Lattice Graphs and Hamming Graphs
Combinatorics, Probability and Computing, 1994In this paper we solve the following problem on the lattice graph L(m1,…,mn) and the Hamming graph H(m1,…,mn), generalizing a result of Felzenbaum-Holzman-Kleitman on the n-dimensional cube (all mi = 2): Characterize the vectors (s1.…,sn) such that there exists a maximum matching in L, respectively, H with exactly si edges in the ith direction.
Aigner, Martin, Klimmek, Regina
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Mathematical Proceedings of the Cambridge Philosophical Society, 1971
1. Tutte(10) has given necessary and sufficient conditions in order that a finite graph have a perfect matching. A different proof was given by Gallai(4). Berge(1) (and Ore (7)) generalized Tutte's result by determining the maximum cardinality of a matching in a finite graph.
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1. Tutte(10) has given necessary and sufficient conditions in order that a finite graph have a perfect matching. A different proof was given by Gallai(4). Berge(1) (and Ore (7)) generalized Tutte's result by determining the maximum cardinality of a matching in a finite graph.
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Canadian Journal of Mathematics, 1974
How large a matching must a graph have?We consider graphs G (finite, undirected, with no loops or multiple edges), with order nG (always ≧ 1) and mG the maximum number of edges in a matching of G. The matchability μG of G is the fraction (2m/n) of nodes covered by a maximum matching.
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How large a matching must a graph have?We consider graphs G (finite, undirected, with no loops or multiple edges), with order nG (always ≧ 1) and mG the maximum number of edges in a matching of G. The matchability μG of G is the fraction (2m/n) of nodes covered by a maximum matching.
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2003
At the prom, 300 students took part. They did not all know each other; in fact, every girl knew exactly 50 boys and every boy knew exactly 50 girls (we assume, as before, that acquaintance is mutual).
L. Lovász, J. Pelikán, K. Vesztergombi
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At the prom, 300 students took part. They did not all know each other; in fact, every girl knew exactly 50 boys and every boy knew exactly 50 girls (we assume, as before, that acquaintance is mutual).
L. Lovász, J. Pelikán, K. Vesztergombi
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Learning Graph Matching with Graph Neural Networks
Graph matching aims at evaluating the dissimilarity of two graphs by defining a constrained correspondence between their nodes and edges. Error-tolerant graph matching, for instance, introduces the concept of a cost for penalizing structural differences in the matching.Kalvin Dobler, Kaspar Riesen
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2009
Application domains such as bioinformatics and web technology represent complex objects as graphs where nodes represent basic objects (i.e. atoms, web pages etc.) and edges model relations among them. In biochemical databases proteins are naturally represented as labeled graphs: the nodes are atoms and the edges are chemical links.
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Application domains such as bioinformatics and web technology represent complex objects as graphs where nodes represent basic objects (i.e. atoms, web pages etc.) and edges model relations among them. In biochemical databases proteins are naturally represented as labeled graphs: the nodes are atoms and the edges are chemical links.
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