Download Vitaly I. Voloshin-Introduction to Graph Theory-Nova (2009) PDF

TitleVitaly I. Voloshin-Introduction to Graph Theory-Nova (2009)
TagsDiscrete Mathematics Vertex (Graph Theory) Theoretical Computer Science Combinatorics
File Size858.0 KB
Total Pages157
Table of Contents
                            INTRODUCTION TO GRAPH THEORY
Contents
Preface
Chapter 1: Basic Definitions and Concepts
	1.1. Fundamentals
	1.2. Graph Modeling Applications
	1.3. Graph Representations
	1.4. Generalizations
	1.5. Basic Graph Classes
	1.6. Basic Graph Operations
	1.7. Basic Subgraphs
	1.8. Separation and Connectivity
Chapter 2: Trees and Bipartite Graphs
	2.1. Trees and Cyclomatic Number
	2.2. Trees and Distance
	2.3. Minimum Spanning Tree
	2.4. Bipartite Graphs
Chapter 3: Chordal Graphs
	3.1. Preliminary
	3.2. Separators and Simplicial Vertices
	3.3. Degrees
	3.4. Distances in Chordal Graphs
	3.5. Quasi-triangulated Graphs
Chapter 4: Planar Graphs
	4.1. Plane and Planar Graphs
	4.2. Euler’s Formula
	4.3. K5 and K3,3 Are not Planar Graphs
	4.4. Kuratowski’s Theorem and Planarity Testing
	4.5. Plane Triangulations and Dual Graphs
Chapter 5: Graph Coloring
	5.1. Preliminary
	5.2. Definitions and Examples
	5.3. Structure of Colorings
	5.4. Chromatic Polynomial
	5.5. Coloring Chordal Graphs
	5.6. Coloring Planar Graphs
	5.7. Perfect Graphs
	5.8. Edge Coloring and Vizing’s Theorem
	5.9. Upper Chromatic Index
Chapter 6: Graph Traversals and Flows
	6.1. Eulerian Graphs
	6.2. Hamiltonian Graphs
	6.3. Network Flows
Chapter 7: Appendix
	7.1. What Is Mathematical Induction
	7.2. Graph Theory Algorithms and Their Complexity
	7.3. Answers and Hints to Selected Exercises
	7.4. Glossary of Additional Concepts
References
Index
                        

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