Graph theory : a problem oriented approach / Daniel A. Marcus.

Format:

Book

Author/Creator:

Marcus, Daniel A., 1945- author.

Contributor:

Mathematical Association of America.

Series:

AMS/MAA Textbooks, 2577-1213 ; v. 53

Language:

English

Subjects (All):

Graph theory.

Graph theory--Problems, exercises, etc.

Physical Description:

1 online resource (xvi, 205 pages)

Place of Publication:

Washington, D.C. : Mathematical Association of America, c2008

System Details:

Mode of access : World Wide Web

Summary:

"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.

Contents:

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

Notes:

Includes index.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2020

Description based on print version record.

Other Format:

Print version: Marcus, Daniel A., 1945- Graph theory :

ISBN:

9781470451851 (online)

Access Restriction:

Restricted for use by site license.