A First Course in Graph Theory

Content: Cover Page
 Title Page
 Copyright Page
 Dedication
 Contents
 Preface
 1. Introduction
 1.1. Graphs and Graph Models
 1.2. Connected Graphs
 1.3. Common Classes of Graphs
 1.4. Multigraphs and Digraphs
 2. Degrees
 2.1. The Degree of a Vertex
 2.2. Regular Graphs
 2.3. Degree Sequences
 2.4. Excursion: Graphs and Matrices
 2.5. Exploration: Irregular Graphs
 3. Isomorphic Graphs
 3.1. The Definition of Isomorphism
 3.2. Isomorphism as a Relation
 3.3. Excursion: Graphs and Groups
 3.4. Excursion: Reconstruction and Solvability
 4. Trees
 4.1. Bridges
 4.2. Trees. 4.3. The Minimum Spanning Tree Problem4.4. Excursion: The Number of Spanning Trees
 5. Connectivity
 5.1. Cut-Vertices
 5.2. Blocks
 5.3. Connectivity
 5.4. Menger\'s Theorem
 5.5. Exploration: Powers and Edge Labelings
 6. Traversability
 6.1. Eulerian Graphs
 6.2. Hamiltonian Graphs
 6.3. Exploration: Hamiltonian Walks
 6.4. Excursion: Early Books of Graph Theory
 7. Digraphs
 7.1. Strong Digraphs
 7.2. Tournaments
 7.3. Excursion: Decision-Making
 7.4. Exploration: Wine Bottle Problems
 8. Matchings and Factorization
 8.1. Matchings
 8.2. Factorization. 8.3. Decompositions and Graceful Labelings8.4. Excursion: Instant Insanity
 8.5. Excursion: The Petersen Graph
 8.6. Exploration: Bi-Graceful Graphs
 9. Planarity
 9.1. Planar Graphs
 9.2. Embedding Graphs on Surfaces
 9.3. Excursion: Graph Minors
 9.4. Exploration: Embedding Graphs in Graphs
 10. Coloring Graphs
 10.1. The Four Color Problem
 10.2. Vertex Coloring
 10.3. Edge Coloring
 10.4. Excursion: The Heawood Map Coloring Theorem
 10.5. Exploration: Modular Coloring
 11. Ramsey Numbers
 11.1. The Ramsey Number of Graphs
 11.2. Turan\'s Theorem
 11.3. Exploration: Modified Ramsey Numbers. 11.4. Excursion: Erdős Numbers12. Distance
 12.1. The Center of a Graph
 12.2. Distant Vertices
 12.3. Excursion: Locating Numbers
 12.4. Excursion: Detour and Directed Distance
 12.5. Exploration: Channel Assignment
 12.6. Exploration: Distance Between Graphs
 13. Domination
 13.1. The Domination Number of a Graph
 13.2. Exploration: Stratification
 13.3. Exploration: Lights Out
 13.4. Excursion: And Still It Grows More Colorful
 Appendix 1. Sets and Logic
 Appendix 2. Equivalence Relations and Functions
 Appendix 3. Methods of Proof
 Solutions and Hints for Odd-Numbered Exercises.