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Introduction to Graph and Hypergraph Theory
 Retail Price: \$135.00 10% Online Discount You Pay: \$121.50
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 Authors: Vitaly I. Voloshin ( Dept. of Mathematics, Physics and Computer Science, Troy Univ., Troy, AL) Book Description: Click here for a review of this title This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalization of Part I. The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph coloring. The second part considers generalizations of Part I and discusses hypertrees, bipartite hypergraphs, hypercycles, chordal hypergraphs, planar hypergraphs and hypergraph coloring. There is an interaction between the parts and within the parts to show how ideas of generalizations work. The main point is to exhibit the ways of generalizations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hypergraphs. This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hypergraphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view. We’ve partnered with Copyright Clearance Center to make it easy for you to request permissions to reuse Nova content. For more information, click here or click the "Get Permission" button below to link directly to this book on Copyright Clearance Center's website.

 Table of Contents: Preface pp. i-xiv I. Graphs pp.1-4 1. Basic Definitions and Concepts pp.5-5 1.1 Fundamentals pp.5-7 1.2 Graph modeling applications pp.8-11 1.3 Graph representations pp..12-14 1.4 Generalizations pp.15-17 1.5 Basic graph classes pp.18-24 1.6 Basic graph operations pp.25-28 1.7 Basic subgraphs pp.29-33 1.8 Separation and connectivity pp.34-38 2. Trees and Bipartite Graphs pp.39-39 2.1 Trees and cyclomatic number pp.39-40 2.2 Trees and distance pp.41-42 2.3 Minimum spanning tree pp.43-44 2.4 Bipartite graphs pp.45-50 3. Chordal Graphs pp.51-51 3.1 Preliminary pp.51-51 3.2 Separators and simplicial vertices pp.52-56 3.3 Degrees pp.57-58 3.4 Distances in chordal graphs pp.59-61 3.5 Quasi-triangulated graphs pp.62-66 4. Planar Graphs pp.67-67 4.1 Plane and planar graphs pp.67-68 4.2 Euler’s formula pp.69-70 4.3 K5 and K3 3 are not planar graphs pp.71-72 4.4 Kuratowski’s theorem and planarity testing pp.73-75 4.5 Plane triangulations and dual graphs pp.76-78 5. Graph Coloring pp.79-79 5.1 Preliminary pp.79-79 5.2 Definitions and examples pp.80-82 5.3 Structure of colorings pp.83-88 5.4 Chromatic polynomial pp.89-94 5.5 Coloring chordal graphs pp.95-101 5.6 Coloring planar graphs pp.102-107 5.7 Perfect graphs pp.108-111 5.8 Edge coloring and Vizing’s theorem pp.112-115 5.9 Upper chromatic index pp.116-122 6. Traversals and Flows pp.123-123 6.1 Eulerian graphs pp.123-124 6.2 Hamiltonian graphs pp.125-126 6.3 Network flows pp.127-130 II. Hypergraphs pp.131-134 7. Basic Hypergraph Concepts pp.135-135 7.1 Preliminary definitions pp.135-138 7.2 Incidence and duality pp.139-143 7.3 Basic hypergraph classes pp.144-145 7.4 Basic hypergraph operations pp.146-150 7.5 Subhypergraphs pp.151-153 7.6 Conformality and Helly property pp.154-160 8. Hypertrees and Chordal Hypergraphs pp.161-161 8.1 Hypertrees and chordal conformal hypergraphs pp.161-167 8.2 Algorithms on hypertrees pp.168-173 8.3 Cyclomatic number of a hypergraph pp.174-180 9. Some Other Remarkable Hypergraph Classes pp.181-181 9.1 Balanced hypergraphs pp.181-182 9.2 Interval hypergraphs pp.183-184 9.3 Normal hypergraphs pp.185-186 9.4 Planar hypergraphs pp.187-192 10. Hypergraph Coloring pp.193-193 10.1 Basic kinds of classic hypergraph coloring pp.193-196 10.2 Greedy algorithm for the lower chromatic number pp.197-200 10.3 Basic definitions of mixed hypergraph coloring pp.201-206 10.4 Greedy algorithm for the upper chromatic number pp.207-212 10.5 Splitting-contraction algorithm pp.213-218 10.6 Uncolorability pp.219-226 10.7 Unique colorability pp.227-235 10.8 Perfection pp.236-243 10.9 Chromatic spectrum pp.244-253 10.10 Coloring planar hypergraphs pp.254-262 11. Modeling with Hypergraphs pp.263-263 11.1 List colorings without lists pp.263-263 11.2 Resource allocation pp.264-266 12 Appendix pp.267-267 12.1 What is mathematical induction pp.267-268 12.2 Graph Theory algorithms and their complexity pp.269-269 12.3 Answers and hints to selected exercises pp.270-274 12.4 Glossary of additional concepts pp.275-278 References. pp.279-280 Index. pp.281-287

Binding: Hardcover
Pub. Date: 2012
Pages: 301
ISBN: 978-1-60692-372-6
Status: AV

 Status Code Description AN Announcing FM Formatting PP Page Proofs FP Final Production EP Editorial Production PR At Prepress AP At Press AV Available

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