We will show that the smallest polyominoes with Δ = 0 to have no perfect matchings are of order 14 ... new conclusions for the existence of perfect matchings in a ...
Let P be a given polyomino and e be a given edge of P. A simple algorithm is developed for calculating the numbers m(P) and m(P,e) of all perfect matchings of P ...
Jun 19, 2016 · For a polyomino graph H , we show that for every perfect matching M of H with the maximum or second maximum forcing number, f ( H , M ) is equal ...
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In this paper necessary and sufficient conditions are given for a generalized polyomino graph to have a perfect matching and to be elementary, respectively.
Dec 23, 2020 · Abstract. The forcing number of a perfect matching M in a graph G is the smallest number of edges inside M that can not be contained in ...
For a polyomino graph H , we show that for every perfect matching M of H with the maximum or second maximum forcing number, f ( H , M ) is equal to the maximum ...
In the first part of this paper we establish sharp lower bounds on the number of perfect matchings in benzenoid graphs and polyominoes.
of perfect matchings in some special polyominoes. LATTICE ANIMALS AND EAR DECOMPOSITIONS. A perfect matching in a graph G is a collection M of edges of G ...
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Apr 24, 2023 · The L sequence from Section 4 has an interpretation in terms of perfect matchings. To see why, suppose we have a tiling of the Aztec diamond of ...
flip around a face of G which is not a hole. In this paper, we give a necessary and sufficient condition to decide if two perfect matchings of G are in the ...