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A Maximum Resonant Set of Polyomino Graphs

Heping Zhang, Xiangqian Zhou (2016)

Discussiones Mathematicae Graph Theory

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. In this paper,...

A Metaheuristic Approach to Solving the Generalized Vertex Cover Problem

Milanović, Marija (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 90C27, 05C85, 90C59The topic is related to solving the generalized vertex cover problem (GVCP) by genetic algorithm. The problem is NP-hard as a generalization of well-known vertex cover problem which was one of the first problems shown to be NP-hard. The definition of the GVCP and basics of genetic algorithms are described. Details of genetic algorithm and numerical results are presented in [8]. Genetic algorithm obtained high quality solutions in a short period of time.

A Method for Classification of Doubly Resolvable Designs and Its Application

Zhelezova, Stela (2011)

Serdica Journal of Computing

This article presents the principal results of the Ph.D. thesis Investigation and classification of doubly resolvable designs by Stela Zhelezova (Institute of Mathematics and Informatics, BAS), successfully defended at the Specialized Academic Council for Informatics and Mathematical Modeling on 22 February 2010.The resolvability of combinatorial designs is intensively investigated because of its applications. This research focuses on resolvable designs with an additional property - they have resolutions...

A method of constructing the frame of a directed graph

Ichiro Hofuku, Kunio Oshima (2013)

International Journal of Applied Mathematics and Computer Science

In web search engines, such as Google, the ranking of a particular keyword is determined by mathematical tools, e.g., Pagerank or Hits. However, as the size of the network increases, it becomes increasingly difficult to use keyword ranking to quickly find the information required by an individual user. One reason for this phenomenon is the interference of superfluous information with the link structure. The World Wide Web can be expressed as an enormous directed graph. The purpose of the present...

A metric for graphs

Vladimír Baláž, Jaroslav Koča, Vladimír Kvasnička, Milan Sekanina (1986)

Časopis pro pěstování matematiky

A metric graph satisfying [...] w 4 1 = 1 w 4 1 = 1 that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 dim ( W 4 1 ) = 1

Marc Coppens (2016)

Open Mathematics

For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1 w 4 1 = 1 such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

A metric on a system of ordered sets

Alfonz Haviar, Pavel Klenovčan (1996)

Mathematica Bohemica

In [3] a metric on a system of isomorphism classes of ordered sets was defined. In this paper we define another metric on the same system and investigate some of its properties. Our approach is motivated by a problem from practice.

A minimal Set of Generators for the Ring of multisymmetric Functions

David Rydh (2007)

Annales de l’institut Fourier

The purpose of this article is to give, for any (commutative) ring A , an explicit minimal set of generators for the ring of multisymmetric functions T S A d ( A [ x 1 , ⋯ , x r ] ) = A [ x 1 , ⋯ , x r ] ⊗ A d 𝔖 d as an A -algebra. In characteristic zero, i.e. when A is a ℚ -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...

A model theory approach to structural limits

Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)

Commentationes Mathematicae Universitatis Carolinae

The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.

A modification of the median of a tree

Bohdan Zelinka (1993)

Mathematica Bohemica

The concept of median of a tree is modified, considering only distances from the terminal vertices instead of distances from all vertices.

A moment sequence in the q-world

Anna Kula (2007)

Banach Center Publications

The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called q-calculus. A characterization of such a q-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the q-situation. This makes a link between q-positive definiteness and q-complete...

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