Introduction to graph theory
著者
書誌事項
Introduction to graph theory
Prentice Hall, c2001
2nd ed
大学図書館所蔵 全24件
注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
For undergraduate or graduate courses in Graph Theory in departments of mathematics or computer science.
This text offers a comprehensive and coherent introduction to the fundamental topics of graph theory. It includes basic algorithms and emphasizes the understanding and writing of proofs about graphs. Thought-provoking examples and exercises develop a thorough understanding of the structure of graphs and the techniques used to analyze problems. The first seven chapters form the basic course, with advanced material in Chapter 8.
目次
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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