Synopses & Reviews
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.
Synopsis
Since the original four-color problem was introduced in 1852, the field of graph colorings has grown to become one of the most studied areas of graph theory. This book explores the connections between major topics in graph theory and graph colorings as well as emerging concepts, such as geodetic colorings, Ramsey numbers, and coloring extensions. The wide range of applications presented emphasizes the use of algorithms for graph colorings. Each section in the text offers exercises of varying difficulty levels, along with detailed examples and historical references to notable mathematicians. In addition, every chapter provides suggestions for student research projects to encourage further study.
Synopsis
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. This book introduces graph theory with a coloring theme. It explores connections between major topics in graph theory and graph colorings, including Ramsey numbers and domination, as well as emerging topics, such as list colorings, rainbow colorings, distance colorings related to the channel assignment problem, and vertex/edge distinguishing colorings. The authors include historical, applied, and algorithmic discussions. Each chapter contains many exercises of varying levels of difficulty. The text also provides an appendix of suggestions for study projects.