ABSTRACT

Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction.

A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms.

Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.

chapter 1|22 pages

Graphs and Their Complements

chapter 2|24 pages

Paths and Walks

chapter 3|16 pages

Some Special Classes of Graphs

chapter 4|26 pages

Trees and Cycles

chapter 5|30 pages

The Structure of Trees

chapter 6|20 pages

Connectivity

chapter 7|22 pages

Alternating Paths and Matchings

chapter 8|30 pages

Network Flows

chapter 9|36 pages

Hamilton Cycles

chapter 10|22 pages

Digraphs

chapter 11|30 pages

Graph Colorings

chapter 12|52 pages

Planar Graphs

chapter 13|60 pages

Graphs and Surfaces

chapter 14|30 pages

Linear Programming

chapter 15|32 pages

The Primal-Dual Algorithm

chapter 16|20 pages

Discrete Linear Programming