Counting perfect matchings in polyominoes with an application to the dimer problem
P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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Tošić, Ratko, Vojvodić, Dušan (2000)
Novi Sad Journal of Mathematics
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G. L. Garg, B. Kumar (1989)
Matematički Vesnik
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M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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Ivan Gutman (1989)
Publications de l'Institut Mathématique
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Igor E. Zverovich (2006)
Discussiones Mathematicae Graph Theory
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We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that (a) C does not include all perfect graphs and (b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C? A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph...
Min Tang, Xiao-Zhi Ren, Meng Li (2013)
Colloquium Mathematicae
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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
Tomohiro Yamada (2005)
Colloquium Mathematicae
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We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.
Tomislav Doslić (2005)
Discussiones Mathematicae Graph Theory
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It is shown in this note that some matching-related properties of graphs, such as their factor-criticality, regularizability and the existence of perfect 2-matchings, are preserved when iterating Mycielski's construction.
Jinfeng Liu, Xiumei Wang (2014)
Discussiones Mathematicae Graph Theory
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A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered
Heping Zhang, Xiangqian Zhou (2016)
Discussiones Mathematicae Graph Theory
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A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. A dimer covering of P corresponds to a perfect matching. Different dimer coverings can interact via an alternating cycle (or square) with respect to them. A set of disjoint squares of P is a resonant set if P has a perfect matching M so that each one of those squares is M-alternating....
M. Chrobak, S. Poljak (1987)
Applicationes Mathematicae
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Ivan Gutman, Jerzy Cioslowski (1987)
Publications de l'Institut Mathématique
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