Can be used as a college level text for mathematics, computer science, or engineering students. Also suitable for a general education course at a liberal arts college, or for self-study.
Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The book combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems.
Introduction: Problems of Graph Theory
Trees and Forests
Spanning Tree Algorithms
Hamilton Paths and Cycles
Independence and Covering
Connections and Obstructions
Matching Theory for Bipartite Graphs
Applications of Matching Theory
Network Flow Theory
Flow Problems with Lower Bounds
Answers to Selected Problems
About the Author
Daniel A. Marcus received his PhD from Harvard University. He was a J. Willard Gibbs Instructor at Yale University from 1972-74 and Professor of Mathematics at California State Polytechnic University, Pomona from 1979-2004. Marcus has published research papers in the areas of graph theory, number theory, and combinatorics. He is the author of the following books: Combinatorics: A Problem Oriented Approach (also with the MAA), Differential Equations: An Introduction, and Number Fields.