Hypergraph theory : an introduction

• Main Author: Bretto, Alain
• Format: eBook Book
• Language: English
• Published: Cham Springer 2013; Springer International Publishing AG; Springer International Publishing
• Edition: 1
• Series: Mathematical Engineering
• Subjects: Algorithms; Artificial Intelligence; Communications Engineering, Networks; Computer Science; Data Structures and Algorithms; Discrete Mathematics in Computer Science; Document and Text Processing; Engineering; Graph Theory; Hypergraphs; Mathematical and Computational Engineering; Mathematics
• ISBN: 9783319000794; 3319000799; 3319033700; 9783319033709
• ISSN: 2192-4732; 2192-4740
• DOI: 10.1007/978-3-319-00080-0

This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and kernels. It details applications in telecommunications and parallel data structure modeling.

Table of Contents:

• 6.3 Hypercycles in a Dirhypergraph -- 6.4 Algebraic Representation of Dirhypergraphs -- 6.4.1 Dirhypergraphs Isomorphism -- 6.4.2 Algebraic Representation: Definition -- 6.4.3 Algebraic Representation Isomorphism -- References -- 7 Applications of Hypergraph Theory: A Brief Overview -- 7.1 Hypergraph Theory and System Modeling for Engineering -- 7.1.1 Chemical Hypergraph Theory -- 7.1.2 Hypergraph Theory for Telecomunmications -- 7.1.3 Hypergraph Theory and Parallel Data Structures -- 7.1.4 Hypergraphs and Constraint Satisfaction Problems -- 7.1.5 Hypergraphs and Database Schemes -- 7.1.6 Hypergraphs and Image Processing -- 7.1.7 Other Applications -- References -- Index
• Intro -- Preface -- Acknowledgments -- Contents -- 1 Hypergraphs: Basic Concepts -- 1.1 First Definitions -- 1.2 Example of Hypergraph -- 1.2.1 Simple Reduction 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 -- Groups and Symmetries -- 1.4 Generalization of Hypergraphs -- References -- 2 Hypergraphs: First Properties -- 2.1 Graphs versus Hypergraphs -- 2.1.1 Graphs -- 2.1.2 Graphs and Hypergraphs -- 2.2 Intersecting Families, Helly Property -- 2.2.1 Intersecting Families -- 2.2.2 Helly Property -- 2.3 Subtree Hypergraphs -- 2.4 Conformal Hypergraphs -- 2.5 Stable (or Independent), Transversal and Matching -- 2.5.1 Examples: -- 2.6 König Property and Dual König Property -- 2.7 linear Spaces -- References -- 3 Hypergraph Colorings -- 3.1 Coloring -- 3.2 Particular Colorings -- 3.2.1 Strong Coloring -- 3.2.2 Equitable Coloring -- 3.2.3 Good Coloring -- 3.2.4 Uniform Coloring -- 3.2.5 Hyperedge Coloring -- 3.2.6 Bicolorable Hypergraphs -- 3.3 Graph and Hypergraph Coloring Algorithm -- References -- 4 Some Particular Hypergraphs -- 4.1 Interval Hypergraphs -- 4.2 Unimodular Hypergraphs -- 4.2.1 Unimodular Hypergraphs and Discrepancy of Hypergraphs -- 4.3 Balanced Hypergraphs -- 4.4 Normal 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 -- References -- 5 Reduction-Contraction of Hypergraph -- 5.1 Introduction -- 5.2 Reduction Algorithms -- 5.2.1 A Generic Algorithm -- 5.2.2 A Minimum Spanning Tree Algorithm (HR-MST) -- References -- 6 Dirhypergraphs: Basic Concepts -- 6.1 Basic Definitions -- 6.2 Basic Properties of Directed Hypergraphs