Coloring Mixed Hypergraphs

Theory, Algorithms and Applications

Vitaly I. Voloshin

180 pages, parution le 09/04/2003

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Résumé

The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications.

Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory of colorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring.

The book has broad appeal. It will be of interest to both pure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that may become classic in the future.

Contents

Introduction
The lower chromatic number of a hypergraph
Mixed hypergraphs and the upper chromatic number
Uncolorable mixed hypergraphs
Uniquely colorable mixed hypergraphs
$\mathcal{C}$-perfect mixed hypergraphs
Gaps in the chromatic spectrum
Interval mixed hypergraphs
Pseudo-chordal mixed hypergraphs
Circular mixed hypergraphs
Planar mixed hypergraphs
Coloring block designs as mixed hypergraphs
Modelling with mixed hypergraphs
Bibliography
List of figures
Index

L'auteur - Vitaly I. Voloshin

Vitaly I. Voloshin, Moldovan Academy of Sciences, Kishinev, Republic of Moldova

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Vitaly I. Voloshin
Parution	09/04/2003
Nb. de pages	180
Format	18 x 26
Couverture	Relié
Poids	560g
Intérieur	Noir et Blanc
EAN13	9780821828120
ISBN13	978-0-8218-2812-0