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Once considered an “unimportant” branch of topology, graph theory has come into its own through many important contributions to a wide range of fields — and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; covers design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic.
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- Introduction to Graph Theory
- Basic Concepts in Graph Theory
- Trees and Forests
- Spanning Trees
- Fundamental Properties of Graphs and Digraphs
- Connectivity and Flow
- Planar Graphs
- Graph Coloring
- Coloring Enumerations and Chordal Graphs
- Independence, Dominance, and Matchings
- Cover Parameters and Matching Polynomials
- Graph Counting
- Graph Algorithms
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