Waubonsee Community College

Graph theory, a problem oriented approach, Daniel A. Marcus

eng

illustrations

index present

non fiction

Graph theory

191856279

Daniel A. Marcus

MAA textbooks

a problem oriented approach

"Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in that it 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. This problem-oriented format is intended to promote active involvement by the reader while always providing clear direction. This approach figures prominently on the presentation of proofs, which become more frequent and elaborate as the book progresses. Arguments are arranged in digestible chunks and always appear along with concrete examples to keep the readers firmly grounded in their motivation. Spanning tree algorithms, Euler paths, Hamilton paths and cycles, planar graphs, independence and covering, connections and obstructions, and vertex and edge colorings make up the core of the book. Hall's Theorem, the Konig-Egervary Theorem, Dilworth's Theorem and the Hungarian algorithm to the optional assignment problem, matrices, and Latin squares are also explored."--Back cover

Introduction: Problems of graph theory -- A. Basic concepts -- B. Isomorphic graphs -- C. Bipartite graphs -- D. Trees and forests -- E. Spanning tree algorithms -- F. Euler paths -- G. Hamilton paths and cycles -- H. Planar graphs -- I. Independence and covering -- J. Connections and obstructions -- K. Vertex coloring -- L. Edge coloring -- M. Matching theory for bipartite graphs -- N. Applications of matching theory -- O. Cycle-free digraphs -- P. Network flow theory -- Q. Flow problems with lower bounds -- Answers to selected problems