Introduction to Graph Theory (Classic Version)

This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity.An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs.For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

1. Fundamental Concepts.

What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees and Counting. Directed Graphs.

2. Trees and Distance.

Basic Properties. Spanning Trees and Enumeration. Optimization and Trees.

3. Matchings and Factors.

Matchings and Covers. Algorithms and Applications. Matchings in General Graphs.

4. Connectivity and Paths.

Cuts and Connectivity. k-connected Graphs. Network Flow Problems.

5. Coloring of Graphs.

Vertex Colorings and Upper Bounds. Structure of k-chromatic Graphs. Enumerative Aspects.

6. Planar Graphs.

Embeddings and Euler's Formula. Characterization of Planar Graphs. Parameters of Planarity.

7. Edges and Cycles.

Line Graphs and Edge-Coloring. Hamiltonian Cycles. Planarity, Coloring, and Cycles.

8. Additional Topics (Optional).

Perfect Graphs. Matroids. Ramsey Theory. More Extremal Problems. Random Graphs. Eigenvalues of Graphs.

Appendix A: Mathematical Background.

Appendix B: Optimization and Complexity.

Appendix C: Hints for Selected Exercises.

Appendix D: Glossary of Terms.

Appendix E: Supplemental Reading.

Appendix F: References.

Indices.

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Introduction to Graph Theory (Classic Version)

Summary

Table of Contents

Supplemental Materials