Book:Nora Hartsfield/Pearls in Graph Theory: A Comprehensive Introduction

Subject Matter

 * Graph Theory

Contents

 * Foreword to the Revised Edition
 * Foreword


 * Chapter 1. Basic Graph Theory
 * 1.1 Graphs and Degrees of Vertices
 * 1.2 Subgraphs, Isomorphic Graphs
 * 1.3 Trees


 * Chapter 2. Colorings of Graphs
 * 2.1 Vertex Colorings
 * 2.2 Edge Colorings
 * 2.3 Decompositions and Hamilton Cycles
 * 2.4 More Decomposition


 * Chapter 3. Circuits and Cycles
 * 3.1 Eulerian Circuits
 * 3.2 The Oberwolfach Problem
 * 3.3 Infinite Lattice Graphs


 * Chapter 4. Extremal Problems
 * 4.1 A Theorem of Turan
 * 4.2 Cages
 * 4.3 Ramsey Theory


 * Chapter 5. Counting
 * 5.1 Counting $1$-Factors
 * 5.2 Cayley's Spanning Tree Formula
 * 5.3 More Spanning Trees


 * Chapter 6. Labeling Graphs
 * 6.1 Magic Graphs and Graceful Trees
 * 6.2 Conservative Graphs


 * Chapter 7. Applications and Algorithms
 * 7.1 Spanning Tree Algorithms
 * 7.2 Matchings in Graphs, Scheduling Problems
 * 7.3 Binary Trees and Prefix Codes


 * Chapter 8. Drawings of Graphs
 * 8.1 Planar Graphs
 * 8.2 The Four Color Theorem
 * 8.3 The Five Color Theorem
 * 8.4 Graphs and Geometry


 * Chapter 9. Measurements of Closeness to Planarity
 * 9.1 Crossing Number
 * 9.2 Thickness and Splitting Number
 * 9.3 Heawood's Empire Problem


 * Chapter 10. Graphs on Surfaces
 * 10.1 Rotations of Graphs
 * 10.2 Planar Graphs Revisited
 * 10.3 The Genus of a Graph


 * References
 * Index