A New Upper Bound Of Planer Graphs

A graph is planar if it can be drawn on the plane so that each edge isn’t crossed. An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa’(G) of G is the smallest integer κ such that G has an acyclic edge coloring using κ colors. It was conjectured that Xa(G)≤△(G)+2for any simple graph G with maximum degree△(G). In this paper, we prove that if G is a planar graph, then Xo(G)≤△(G)+6.Chapter1states the origin of acyclic edge coloring concepts and sketches the structure and works of the thesis.Chapter2lists some basic theorems to be used throughout the thesis, and the con-cepts of acyclic edge coloring and acyclic chromatic index.Chapter3is one of the main contents. On the basis of known acyclic chromatic index results, combined with the operator theory, we get some new structures about3-,4-,5-,10-vertex.Chapter4is another main content. According some lemmas in chapter3and some known conclusion and using discharging method we make a change of the upper bound of the acyclic edge coloring of planar graph.