Strong EDGE Chromatic Number Of Planar Graphs With Large Girth

An edge coloring of a graph G is strong if each color class is an induced matching of G. In other words, an edge coloring is called a strong edge coloring if any path with length three has three distinct colors. The smallest number of colors for which a strong edge coloring of a graph G exists is called the strong edge chromatic number, denoted by X’s(G).The strong edge coloring problem is one of the important contents of graph theory, and has a wide range of applications on computer science and network technology, and other fields. It is more difficult to determine strong edge chromatic number, so most of the researches are on the classes of special graphs. In this paper, we first survey the previous researches on this topic, and then we focus on the strong edge chromatic number of planar graphs with large girth. The proof of the main result mainly replies on the structures of odd graphs. We proved that, if G is a planar graph with girth at least 10△(G)+26, then X’s(G)≤2△(G)-1.