Cartesian product of hypergraphs: properties and algorithms

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs

Efficience et volatilité des marchés agricoles spot et à termes: L'impact de la fréquence des transactions

In efficient markets, asset prices are equal to their fundamentals. This classical view is considered valid for agricultural commodities' spot and futures markets. However, fragmentation of orders impacts price dynamics, leading to modification in spot and futures' trade frequency, relative trade frequency, and quantities exchanged. To highlight public policies on the impacts of fragmentation of orders, it is necessary to improve the understanding of its theoretical consequences. Based on a sequential trading framework, our main result showed that unbiased prices and a minimal volatility of fundamental basis are achieved not with optimal trade frequencies but with an optimal relative trade frequency

Contribuciones sobre protección, conservación, investigación y manejo de la vida silvestre y areas naturales : VI reserva natural integral de Somuncurá proyectada en Río Negro (República Argentina)

Fil: Daciuk, Juan. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentin

Mathematical morphology and poset geometry

The aim of this paper is to characterize morphological convex geometries (resp., antimatroids). We define these two structures by using closure operators, and kernel operators. We show that these convex geometries are equivalent to poset geometries

Factorization of products of hypergraphs: Structure and algorithms

International audienceOn the one hand Cartesian products of graphs have been extensively studied since the 1960s. On the other hand hypergraphs are a well-known and useful generalization of graphs. In this article, we present an algorithm able to factorize into its prime factors any bounded-rank and bounded-degree hypergraph in O(nm), where n is the number of vertices and m is the number of hyperedges of the hypergraph. First the algorithm applies a graph factorization algorithm to the 2-section of the hypergraph. Then the 2-section factorization is used to build the factorization of the hypergraph via the factorization of its L2-section. The L2-section is a recently introduced way to interpret a hypergraph as a labeled-graph. The graph factorization algorithm used in this article is due to Imrich and Peterin and is linear in time and space. Nevertheless any other such algorithm could be extended to a hypergraph factorization algorithm similar to the one presented here

Cayley graphs and G-graphs: Some applications

International audienceThis paper introduces some relations about Cayley graphs and G-graphs. We present a sufficient condition to recognize when a G-graph is a Cayley graph. The relation between G-graphs and Cayley graphs allows us to consider some applications to the hamiltonicity of Cayley graphs. In the last section we illustrate our results by showing that some new classes of Cayley graphs are hamiltonian

Hypergraph Theory - An Introduction

International audience"This book addresses the mathematics and theory of hypergraphs. The target audience includes graduate students and researchers with an interest in math and computer science (CS). ... I expect readers of this book will be motivated to advance this field, which in turn can advance other sciences." (Hsun-Hsien Chang, Computing Reviews, January, 2014) "The aim of this book is to introduce the basic concepts of hypergraphs, to present the knowledge of the theory and applications of hypergraphs in other fields. ... This book is useful for anyone who wants to understand the basics of hypergraph theory. It is mainly for math and computer science majors, but it may also be useful for other fields which use the theory. ... appropriate for both researchers and graduate students. It is very well-written and proofs are stated in a clear manner." (Somayeh Moradi, zbMATH, Vol. 1269, 2013