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Coloring Mixed Hypergraphs: Theory, Algorithms and Applications
Vitaly I. Voloshin, Moldovan Academy of Sciences, Kishinev, Republic of Moldova
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
2002; 181 pp; hardcover
Volume: 17
ISBN-10: 0-8218-2812-6
ISBN-13: 978-0-8218-2812-0
List Price: US$57
Member Price: US$45.60
Order Code: FIM/17
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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.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and pure and applied mathematicians interested in discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industry.

Table of 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
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