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PERFECT MATCHINGS AND
"... 1. Introduction A lattice in the plane divides the plane into elementary regions. A tile is the union oftwo elementary regions that share an edge. A region is a connected region in the plane whose boundary consists of lattice segments. A tiling of a region is a way to pair theelementary regions it c ..."
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for studying tiling generating functions is that tilings of lattice regions can be identified with perfect matchings of their dual graphs, and are thereforeinstances of the dimer model of statistical physics on various lattice graphs.
Perfect Matching
"... A matching of a graph is a subset of the edges of that graph, such that no two edges in the matching are incident on the same vertex. A matching is maximal if no edge can be added to the set while still being a matching. A matching is maximum is it has the most edges of any matching. A matching is p ..."
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is perfect (or complete) if every vertex in the graph is incident to an edge in the matching. A
Perfect Matchings and Perfect Powers
 J. ALGEBRAIC COMBIN
, 2003
"... In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers [5][11][8]. In this ..."
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Cited by 12 (2 self)
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In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers [5][11][8]. In this
Perfect Matching Preservers
, 2004
"... For two bipartite graphs G and G 0, a bijection : E(G) ! E(G 0 is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if (M) is a perfect matching in G 0 ..."
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For two bipartite graphs G and G 0, a bijection : E(G) ! E(G 0 is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if (M) is a perfect matching in G 0
On Perfect Matchings in Uniform Hypergraphs with . . .
, 2009
"... We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform hyp ..."
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Cited by 29 (4 self)
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We study sufficient ℓdegree (1 ≤ ℓ < k) conditions for the appearance of perfect and nearly perfect matchings in kuniform hypergraphs. In particular, we obtain a minimum vertex degree condition (ℓ = 1) for 3uniform hypergraphs, which is approximately tight, by showing that every 3uniform
COUNTING PERFECT MATCHINGS
"... Abstract. Let G be a graph on n vertices. A perfect matching of the vertices of G is a collection of n/2 edges whose union is the entire graph. This definition only applies to graphs with an even number of vertices, however. We present a generalization of the notion of a perfect matching to include ..."
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Abstract. Let G be a graph on n vertices. A perfect matching of the vertices of G is a collection of n/2 edges whose union is the entire graph. This definition only applies to graphs with an even number of vertices, however. We present a generalization of the notion of a perfect matching to include
Perfect matchings and the octahedron recurrence
 math.CO/0402452, 2004. André Henriques, Mathematisches Institut, Westfälische WilhelmsUniversität, Einsteinstr. 62, 48149
"... We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conje ..."
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Cited by 50 (1 self)
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and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the Laurent polynomial and the perfect matchings of certain graphs, generalizing the theory of Aztec diamonds. In particular, this shows that the coefficients of this polynomial, and polynomials obtained
Eigenvalues and perfect matchings
 Linear Algebra Appl
"... We give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix. We also show that a distanceregular graph of degree k is kedgeconnected. ..."
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Cited by 5 (0 self)
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We give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix. We also show that a distanceregular graph of degree k is kedgeconnected.
Graphs of Triangulations and Perfect Matchings
 Graphs Combin
, 2005
"... P ) of P has a vertex for every triangulation of P , and two of them are adjacent if they di#er by a single edge exchange. We prove that the subgraph (P ), consisting of all triangulations of P that admit a perfect matching, is connected. A main tool in our proof is a result of independent ..."
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Cited by 4 (2 self)
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P ) of P has a vertex for every triangulation of P , and two of them are adjacent if they di#er by a single edge exchange. We prove that the subgraph (P ), consisting of all triangulations of P that admit a perfect matching, is connected. A main tool in our proof is a result of independent
CYCLES AND PERFECT MATCHINGS
, 2003
"... ... 273290) introduced the cover polynomial for a directed graph and showed that it was connected with classical rook theory. M. Dworkin (J. Combin. Theory Ser. B 71 (1997), 1753) showed that the cover polynomial naturally factors for directed graphs associated with Ferrers boards. The authors (Ad ..."
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(Adv. Appl. Math. 27 (2001), 438481) developed a rook theory for shifted Ferrers boards where the analogue of a rook placement is replaced by a partial perfect matching of K2n, the complete graph on 2n vertices. In this paper, we show that an analogue of Dworkin’s result holds for shifted Ferrers
Results 1  10
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3,103