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.
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