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Chromatic graph theory 1st Edition by Gary Chartrand, Ping Zhang ISBN 1584888016 9781584888017

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Chromatic graph theory 1st Edition Gary Chartrand Digital Instant Download

Author(s): Gary Chartrand, Ping Zhang
ISBN(s): 9781584888017, 1584888016
Edition: 1
File Details: PDF, 3.42 MB
Year: 2009
Language: english
SKU: EB-1006842 Category: Tags: ,

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ISBN 10: 1584888016
ISBN 13: 9781584888017
Author: Gary Chartrand, Ping Zhang

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.

Chromatic graph theory 1st Table of contents:

1. Introduction to Chromatic Graph Theory

  • 1.1 Overview of Graph Theory

  • 1.2 The Importance of Chromatic Graph Theory

  • 1.3 History and Development of Chromatic Theory

  • 1.4 Basic Concepts: Graphs, Vertices, Edges, and Coloring

2. Fundamental Concepts of Graph Coloring

  • 2.1 Definition of Graph Coloring

  • 2.2 Proper Coloring and Chromatic Number

  • 2.3 Types of Graph Colorings

  • 2.4 The Chromatic Polynomial

  • 2.5 The Four Color Theorem

3. Chromatic Numbers and Their Properties

  • 3.1 Upper and Lower Bounds of Chromatic Numbers

  • 3.2 Chromatic Numbers of Specific Graph Classes

  • 3.3 Chromatic Number of Planar Graphs

  • 3.4 Coloring Algorithms and Their Efficiency

  • 3.5 Applications of Chromatic Numbers

4. Advanced Topics in Chromatic Graph Theory

  • 4.1 The Chromatic Index

  • 4.2 Edge Coloring and the Vizing Theorem

  • 4.3 List Coloring and Its Variants

  • 4.4 Total Coloring and the Total Chromatic Number

  • 4.5 Chromatic Spectrum

5. Planar Graphs and Chromatic Graph Theory

  • 5.1 Planar Graphs: Definition and Properties

  • 5.2 The Four Color Theorem and Planarity

  • 5.3 Applications of Chromatic Graph Theory in Planar Graphs

  • 5.4 Colorings in Geometric Graphs

  • 5.5 Challenges and Open Problems in Planar Coloring

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Tags: Gary Chartrand, Ping Zhang, Chromatic graph