Some Equitable Coloring Problems On Graphs

Graph coloring is an important research topic in graph theory, has important the-oretical value and research value, and has been applied in many areas. As an important branch of graph coloring, Equitable Total Coloring is currently in the upsurge of foreign researchers and there are many problems open to study.This paper consists of five parts, mainly discusses some Equitable Total Coloring problems on associated graphs.In Chapter1and Chapter2, we introduce the background of the research pre-sented in the thesis, history of the development of Equitable Total Coloring.In Chapter3, we discuss some basic theory of equitable coloring on graphs. We give two theorems for some simple graphs; we give a theorem about the Equitable Total Coloring of the join graph meeting some special conditions; we also make a preliminary study for equitable coloring on2-degenerate graphs.In Chapter4, we study the equitable list coloring of graphs. Kostochka, Pelsma-jer and West conjectured that for k≥△(G), every graph G is equitably k-choosable. Related to this, we prove a conclusion of outerplanar graphs.In Chapter5, we study the Equitable Coloring on the pain graph and some special graphs.