Hypergraph Theory: An Introduction by Alain Bretto

By Alain Bretto

This booklet offers an advent to hypergraphs, its objective being to beat the shortcoming of modern manuscripts in this concept. within the literature hypergraphs have many different names equivalent to set platforms and households of units. This paintings provides the speculation of hypergraphs in its most unusual facets, whereas additionally introducing and assessing the most recent options on hypergraphs. the range of subject matters, their originality and novelty are meant to assist readers greater comprehend the hypergraphs in all their variety which will understand their worth and gear as mathematical instruments. This publication should be an excellent asset to upper-level undergraduate and graduate scholars in desktop technological know-how and arithmetic. it's been the topic of an annual Master's direction for a few years, making it additionally supreme to Master's scholars in computing device technology, arithmetic, bioinformatics, engineering, chemistry, and plenty of different fields. it's going to additionally profit scientists, engineers and a person else who desires to comprehend hypergraphs theory.

Table of Contents


Hypergraph thought - An Introduction

ISBN 9783319000794 ISBN 9783319000800




1 Hypergraphs: easy Concepts

1.1 First Definitions
1.2 instance of Hypergraph
1.2.1 easy relief Hypergraph Algorithm
1.3 Algebraic Definitions for Hypergraphs
1.3.1 Matrices, Hypergraphs and Entropy
1.3.2 Similarity and Metric on Hypergraphs
1.3.3 Hypergraph Morphism; teams and Symmetries
1.4 Generalization of Hypergraphs

2 Hypergraphs: First Properties

2.1 Graphs as opposed to Hypergraphs
2.1.1 Graphs
2.1.2 Graphs and Hypergraphs
2.2 Intersecting households, Helly Property
2.2.1 Intersecting Families
2.2.2 Helly Property
2.3 Subtree Hypergraphs
2.4 Conformal Hypergraphs
2.5 solid (or Independent), Transversal and Matching
2.5.1 Examples:
2.6 K�nig estate and twin K�nig Property
2.7 linear Spaces

3 Hypergraph Colorings

3.1 Coloring
3.2 specific Colorings
3.2.1 powerful Coloring
3.2.2 Equitable Coloring
3.2.3 strong Coloring
3.2.4 Uniform Coloring
3.2.5 Hyperedge Coloring
3.2.6 Bicolorable Hypergraphs
3.3 Graph and Hypergraph Coloring Algorithm

4 a few specific Hypergraphs

4.1 period Hypergraphs
4.2 Unimodular Hypergraphs
4.2.1 Unimodular Hypergraphs and Discrepancy of Hypergraphs
4.3 Balanced Hypergraphs
4.4 basic Hypergraphs
4.5 Arboreal Hypergraphs, Acyclicity and Hypertree Decomposition
4.5.1 Acyclic Hypergraph
4.5.2 Arboreal and Co-Arboreal Hypergraphs
4.5.3 Tree and Hypertree Decomposition
4.6 Planar Hypergraphs

5 Reduction-Contraction of Hypergraph

5.1 Introduction
5.2 relief Algorithms
5.2.1 A frequent Algorithm
5.2.2 A minimal Spanning Tree set of rules (HR-MST)

6 Dirhypergraphs: simple Concepts

6.1 simple Definitions
6.2 easy homes of Directed Hypergraphs
6.3 Hypercycles in a Dirhypergraph
6.4 Algebraic illustration of Dirhypergraphs
6.4.1 Dirhypergraphs Isomorphism
6.4.2 Algebraic illustration: Definition
6.4.3 Algebraic illustration Isomorphism

7 functions of Hypergraph thought: a quick Overview

7.1 Hypergraph conception and process Modeling for Engineering
7.1.1 Chemical Hypergraph Theory
7.1.2 Hypergraph idea for Telecomunmications
7.1.3 Hypergraph idea and Parallel facts Structures
7.1.4 Hypergraphs and Constraint delight Problems
7.1.5 Hypergraphs and Database Schemes
7.1.6 Hypergraphs and photo Processing
7.1.7 different Applications


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