Graph Theory: A Problem Oriented Approach (Mathematical Association of America Textbooks)

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9780883857533: Graph Theory: A Problem Oriented Approach (Mathematical Association of America Textbooks)
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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.

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Book Description:

Combining the features of a textbook with those of a problem workbook, the material is presented through 360 strategically placed problems explained with helpful notes. Concepts of graph theory are introduced, developed and reinforced by working through these problems, encouraging readers to get actively involved.

About the Author:

Daniel A. Marcus received his Ph.D. from Harvard University. He was a J. Willard Gibbs Instructor at Yale University from 1972-1974. He was Professor of Mathematics at California State Polytechnic University, Pomona from 1979-2004. He 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, Differential Equations: An Introduction, and Number Fields.

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Marcus, Daniel
Published by The Mathematical Association o (2008)
ISBN 10: 0883857537 ISBN 13: 9780883857533
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