Hypergraph theory. An introduction
type: Item
instance of: scholarly article
title: Hypergraph theory. An introduction
zbMATH Open document ID: 1269.05082
DOI: 10.1007/978-3-319-00080-0
author: Alain Bretto
published in: Mathematical Engineering
publication date: 2013-04-04T00:00:00Z
review text: In the past 20 years, hypergraph theory and its applications has been developed rapidly and has been an extremely useful tool for solving problems in many areas such as Combinatorics, Computer Science, Optimization, Operation Research, Algebra, Number Theory, etc. 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. More precisely, the book proceeds as follows. In Chapter 1, basic definitions on hypergraphs are given from graph generalization point of view. Algebraic definitions for hypergraphs such as hypergraph entropy, similarity function, metric on hypergraphs and hypergraph morphism are presented. Chapter 2 is devoted to the study of Helly property and König property on hypergraphs. In Chapter 3, colorings of hypergraphs are discussed. Some particular colorings like strong coloring, equitable coloring, good coloring and uniform coloring are introduced. Some results on bicolorable hypergraphs are given and finally algorithms for coloring of graphs and hypergraphs are presented. Chapter 4 begins with introducing some nice families of hypergraphs which have very nice properties and have useful applications. These, include interval hypergraphs, unimodular hypergraphs, balanced hypergraphs, normal hypergraphs, acyclic hypergraphs and Arboreal hypergraphs. In the sequel, hypertree decomposition is discussed, which has many applications in Computer Science. This chapter ends with planar hypergraphs, which are useful in areas such as VLSI design and databases. In Chapter 5, some reduction algorithms for hypergraphs are introduced. The theory of reduction corresponds a reduced hypergraph to any hypergraph, which has less complexity and preserves many nice properties of the hypergraph. Chapter 6, is devoted to the study of directed hypergraphs. After stating basic concepts, Eulerian dirhypergraphs and algebraic representation of dirhypergraphs are discussed. Chapter…
reviewed by: Somayeh Moradi
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05-01
zbMATH DE Number: 6150272
zbMATH Keywords: hypergraph
zbMATH Keywords: coloring
zbMATH Keywords: dirhypergraph
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-00080-0
OpenAlex ID: W4206255050
description: scientific article; zbMATH DE number 6150272