WITHDRAWN: The study of edge coloring and chromatic graph theory and its applications

Abstract

The field of graph colorings has developed into one of the most popular areas of graph theory. This research 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 such emerging topics as list colorings, rainbow colorings, distance colorings related to the Channel Assignment Problem, and vertex/edge distinguishing colorings. Discussions of a historical, applied, and algorithmic nature are included. For Brooks' Theorem, which says that the chromatic number is at most appropriate in Everything except two of the events. In the case of a 2, 1-colored line, we show the 2, 1- The chromatic number is at most true 2 + . For a graph with a fractional hue, we 're showing that the fractional chromatic number is at most normal.