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 کاملPoint sets with many non-crossing perfect matchings
The maximum number of non-crossing straight-line perfect matchings that a set of n points in the plane can have is known to be O(10.0438) and Ω∗(3n). The lower bound, due to Garćıa, Noy, and Tejel (2000), is attained by the double chain, which has Θ(3/n) such matchings. We reprove this bound in a simplified way that uses the novel notion of down-free matchings. We then apply this approach to se...
متن کاملPerfect Matchings and Perfect Powers
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 (N. Elkies et al., J. Algebraic Combin. 1 (1992), 111– 132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this pa...
متن کاملPerfect Matchings and Perfect Squares
In 1961, P.W. Kasteleyn enumerated the domino tilings of a 2n × 2n chessboard. His answer was always a square or double a square (we call such a number "squarish"), but he did not provide a combinatorial explanation for this. In the present thesis, we prove by mostly combinatorial arguments that the number of matchings of a large class of graphs with 4-fold rotational symmetry is squarish; our ...
متن کاملSome perfect matchings and perfect half-integral matchings in NC
We show that for any class of bipartite graphs which is closed under edge deletion and where the number of perfect matchings can be counted in NC, there is a deterministic NC algorithm for finding a perfect matching. In particular, a perfect matching can be found in NC for planar bipartite graphs and K3,3-free bipartite graphs via this approach. A crucial ingredient is part of an interior-point...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1995
ISSN: 0304-3975
DOI: 10.1016/0304-3975(94)00289-u