Nova Publishers
My Account Nova Publishers Shopping Cart
HomeBooksSeriesJournalsReference CollectionseBooksInformationSalesImprintsFor Authors
  Top » Catalog » Books » Mathematics and Statistics » My Account  |  Cart Contents  |  Checkout   
Quick Find
Use keywords to find the product you are looking for.
Advanced Search
What's New? more
Fetal Alcohol Syndrome: Recognition, Differential Diagnosis and Long-Term Effects
Shopping Cart more
0 items
Shipping & Returns
Privacy Notice
Conditions of Use
Contact Us
01.Algebra for Athletes 2nd Edition
02.Advanced Mathematics for Engineers with Applications in Stochastic Processes
03.Dynamic Fuzzy Logic and its Applications
04.Advanced Mathematics for Engineers with Applications in Stochastic Processes
05.How to Solve Problems: New Methods and Ideas
06.Introduction to Graph and Hypergraph Theory
07.Engineering Perspectives of Human Society: Application of Control Theory, Game Theory, and Information Theory to Social Phenomena
08.Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing
09.The Mathematics of the Periodic Table
10.Progress in Neurocomputing Research
Notifications more
NotificationsNotify me of updates to Introduction to Graph and Hypergraph Theory
Tell A Friend
Tell someone you know about this product.
Introduction to Graph and Hypergraph Theory
Retail Price: $135.00
10% Online Discount
You Pay:

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
Customers who bought this product also purchased
A System Architecture Approach to the Brain: From Neurons to Consciousness
A System Architecture Approach to the Brain: From Neurons to Consciousness
Autonomous Robots Research Advances
Autonomous Robots Research Advances
Foundations and Applications of Variational and Perturbation Methods
Foundations and Applications of Variational and Perturbation Methods
Nanotechnology Research Developments
Nanotechnology Research Developments
Recessions: Prospects and Developments
Recessions: Prospects and Developments
A Computable General Equilibrium Model for Environmental Policy Analysis: The Case of Deforestation in the Philippines
A Computable General Equilibrium Model for Environmental Policy Analysis: The Case of Deforestation in the Philippines
Special Focus Titles
01.Violent Communication and Bullying in Early Childhood Education
02.Cultural Considerations in Intervention with Women and Children Exposed to Intimate Partner Violence
03.Chronic Disease and Disability: The Pediatric Lung
04.Fruit and Vegetable Consumption and Health: New Research
05.Fire and the Sword: Understanding the Impact and Challenge of Organized Islamism. Volume 2

Nova Science Publishers
© Copyright 2004 - 2022

Introduction to Graph and Hypergraph Theory