1. Fundamental concepts: What is a graph? -- 2. Trees and distance: Basic properties -- 3. Matchings and factors: Matchings and covers -- 4. Connectivity and paths: Cuts and connectivity -- 5. Coloring of graphs: Vertex colorings and upper bounds -- 6. Planar graphs: Embeddings and Euler's formula -- 7. Edges and cycles: Line graphs and edge-coloring -- 8. Additional topics (optional): Perfect graphs --

The main objective of this book is to develop a thorough understanding of the structure of graphs and the techniques used to analyze problems in graph theory. Fundamental graph algorithms are also included. Numerous examples, illustrations, and exercises guide readers through the concepts and proofs. Offers a comprehensive and up-to-date presentation of the fundamental topics in graph theory. Features an early review of basic proof techniques. Structures content for intellectual coherence, providing a gradual increase in intellectual and complexity throughout the book. Introduces new concepts as needed; presents concepts and results in clearly defined units; provides illustrations for key steps in many proofs.