Introduction to Graph Theory

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.