Graph Edge Coloring - by Michael Stiebitz & Diego Scheide & Bjarne Toft & Lene M Favrholdt (Hardcover)

About the Book

"Written by world authorities on graph theory, this book features many new advances and applications in graph edge coloring, describes how the results are interconnected, and provides historial context throughout. Chapter coverage includes an introduction to coloring preliminaries and lower and upper bounds; the Vizing fan; the Kierstead path; simple graphs and line graphs of multigraphs; the Tashkinov tree; Goldberg's conjecture; extreme graphs; generalized edge coloring; and open problems. It serves as a reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization, as well as a graduate-level course book for students of mathematics, optimization, and computer science"-- Provided by publisher.

From the Back Cover

Features recent advances and new applications in graph edge coloring

Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring.

The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as:

• Use of Tashkinov trees to obtain an asymptotic positive solution to Goldberg's conjecture

• Application of Vizing fans to obtain both known and new results

• Kierstead paths as an alternative to Vizing fans

• Classification problem of simple graphs

• Generalized edge coloring in which a color may appear more than once at a vertex

This book also features first-time English translations of two groundbreaking papers written by Vadim Vizing on an estimate of the chromatic class of a p-graph and the critical graphs within a given chromatic class.

Written by leading experts who have reinvigorated research in the field, Graph Edge Coloring is an excellent book for mathematics, optimization, and computer science courses at the graduate level. The book also serves as a valuable reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization.

Review Quotes

"College mathematics collections need just this sort of rarity-accounts of major unsolved problems, elementary but still comprehensive. Summing Up: Recommended. Upper-division undergraduates." (Choice, 1 September 2012)

About the Author

Michael Stiebitz, PhD, is Professor of Mathematics at the Technical University of Ilmenau, Germany. He is the author of numerous journal articles in his areas of research interest, which include graph theory, combinatorics, cryptology, and linear algebra.

Diego Scheide, PhD, is a Postdoctoral Researcher in the Department of Mathematics at Simon Fraser University, Canada.

Bjarne Toft, PhD, is Associate Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark.

Lene M. Favrholdt, PhD, is Associate Professor in the Department of Mathematics and Computer Science at the University of Southern Denmark.