Chromatic Graph Theory

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CRC Press, Sep 22, 2008 - Mathematics - 504 pages
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Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.

This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.

With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.

 

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Contents

The Origin of Graph Colorings
1
Introduction to Graphs
27
Trees and Connectivity
53
Eulerian and Hamiltonian Graphs
71
Matchings and Factorization
91
Graph Embeddings
109
Introduction to Vertex Colorings
147
Bounds for the Chromatic Number
175
Monochromatic and Rainbow Colorings
289
Complete Colorings
329
Distinguishing Colorings
359
Colorings Distance and Domination
397
Study Projects
439
General References
446
Bibliography
453
Index
465

Coloring Graphs on Surfaces
205
Restricted Vertex Colorings
223
Edge Colorings of Graphs
249

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About the author (2008)

For the last several years, Ping Zhang has been an indefatigable proponent for HCI in the IS discipline. She has organized tracks at the major IS conferences, published research in prominent journals, and is now pushing to add the course to the required IS curriculum. She has become the "face of HCI" in the IS community. Ping earned her PhD in MIS at UT-Austin and teaches at the School of Information Studies at Syracuse University.

Her co-authors Dov Te'eni and Jane Carey have been writing in the area for many years. Te'eni received his PhD in MIS from Tel Aviv University and teaches at Bar Ilan University in Israel. He spent several years teaching at Case Western and has been a visiting professor at Yale and NYU, Oxford and Warwick in the UK, and Waterloo in Canada. He is well connected to the worldwide IS community and attends all major IS conferences. Carey received her PhD at the University of Mississippi and teaches at ASU-West after four years at Texas A&M.

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