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Displaying similar documents to “Bounds for the Number of Perfect Matchings in Hexagonal Systems”

Odd perfect numbers of a special form

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.

Mycielskians and matchings

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.

On near-perfect and deficient-perfect numbers

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.

On a perfect problem

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...

A note on pm-compact bipartite graphs

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

A Maximum Resonant Set of Polyomino Graphs

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....

On a sum of divisors problem.

De Koninck, Jean-Marie, Ivić, Aleksandar (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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