Fractional Graph Theory: A Rational Approach to the Theory of Graphs (Dover Books on Mathematics) - Softcover

Prof. Edward R. Scheinerman; Daniel H. Ullman

Softcover

ISBN 10: 0486485935 ISBN 13: 9780486485935

Publisher: Dover Publications, 2013

Synopsis

A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers, and fractional aspects of partially ordered sets.
Challenging exercises reinforce the contents of each chapter, and the authors provide substantial references and bibliographic materials. A comprehensive reference for researchers, this volume also constitutes an excellent graduate-level text for students of graph theory and linear programming.

About this title

From the Publisher

The vast majority of concepts in graph theory are whole-number based. Invariants from chromatic number to arboricity only take on integer values. In this book the authors explore generalizations of core graph theory notions by allowing real values to substitute where normally only integers would be permitted. The aim is to prove "fractional analogues" of the theorems of traditional graph theory.

From the Back Cover

"Both authors are excellent expositors-exceptionally so-and this makes for a pleasurable read and allows for clear understanding of the mathematical concepts." -Joel Spencer Fractional Graph Theory explores the various ways in which integer-valued graph theory concepts can be modified to derive nonintegral values. Based on the authors' extensive review of the literature, it provides a unified treatment of the most important results in the study of fractional graph concepts. Professors Scheinerman and Ullman begin by developing a general fractional theory of hypergraphs and move on to provide in-depth coverage of fundamental and advanced topics, including fractional matching, fractional coloring, and fractional edge coloring; fractional arboricity via matroid methods; and fractional isomorphism. The final chapter is devoted to a variety of additional issues, such as fractional topological graph theory, fractional cycle double covers, fractional domination, fractional intersection number, and fractional aspects of partially ordered sets. Supplemented with many challenging exercises in each chapter as well as an abundance of references and bibliographic material, Fractional Graph Theory is a comprehensive reference for researchers and an excellent graduate-level text for students of graph theory and linear programming.

Edition details

• Publisher: Dover Publications
• Publication date: 2013
• ISBN 10: 0486485935
• ISBN 13: 9780486485935
• Binding: Paperback
• Language: English
• Number of pages: 240