On the number of perfect matchings of line graphs
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...
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Let f(n, p) denote the maximum number of edges in a graph having n vertices and exactly p perfect matchings. For fixed p, Dudek and Schmitt showed that f(n, p) = n2/4 + cp for some constant cp when n is at least some constant np. For p ≤ 6, they also determined cp and np. For fixed p, we show that the extremal graphs for all n are determined by those with O( √ p) vertices. As a corollary, a com...
متن کاملPerfect Matchings of Line Graphs with Small Maximum Degree
Let G be a connected graph with vertex set V (G) = {v1, v2, · · · , vν} , which may have multiple edges but have no loops, and 2 ≤ dG(vi) ≤ 3 for i = 1, 2, · · · , ν, where dG(v) denotes the degree of vertex v of G. We show that if G has an even number of edges, then the number of perfect matchings of the line graph of G equals 2, where n is the number of 3-degree vertices of G. As a corollary,...
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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...
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Let G be a graph embedded in a surface and let F be a set of even faces of G (faces bounded by a cycle of even length). The resonance graph of G with respect to F, denoted by R(G;F), is a graph such that its vertex set is the set of all perfect matchings of G and two vertices M1 and M2 are adjacent to each other if and only if the symmetric difference M1 ⊕M2 is a cycle bounding some face in F. ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.10.032