Perfect Matchings and Applications
نویسندگان
چکیده
منابع مشابه
Perfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملPerfect Matchings of Cellular Graphs
We introduce a family of graphs, called cellular, and consider the problem of enumerating their perfect matchings. We prove that the number of perfect matchings of a cellular graph equals a power of 2 tiroes the number of perfect matchings of a certain subgraph, called the core of the graph. This yields, as a special case, a new proof of the fact that the Aztec diamond graph of order n introduc...
متن کاملComplete forcing numbers of polyphenyl systems
The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...
متن کاملApplications of graphical condensation for enumerating matchings and tilings
A technique called graphical condensation is used to prove various combinatorial identities among numbers of (perfect) matchings of planar bipartite graphs and tilings of regions. Graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph, and then re-partitioning the united matching (actually a multigraph) into matchings of two other subgraphs, in o...
متن کاملMaximum matchings in scale-free networks with identical degree distribution
The size and number of maximum matchings in a network have found a large variety of applications in many fields. As a ubiquitous property of diverse real systems, power-law degree distribution was shown to have a profound influence on size of maximum matchings in scale-free networks, where the size of maximum matchings is small and a perfect matching often does not exist. In this paper, we stud...
متن کاملGraphical condensation of plane graphs: A combinatorial approach
The method of graphical vertex-condensation for enumerating perfect matchings of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003), 267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57) and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-cond...
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تاریخ انتشار 2010