List Strong Edge Coloring Of Planar Graphs With Maximum Degree 4

In this paper,we mainly give a upper bound for list strong edge coloring of planar graphs with maximum degree 4.The edge coloring problem is to color all edges,such that any two adjacent edges have two different colors.Strong edge coloring is based on edge coloring,but it requires that any path of length 3 have 3 different colors.List strong edge coloring is a generalized strong edge coloring,we give a list of colors,named as L（e）,to each edge in graph G,and in the way of coloring we only can use the color in L（e） to color edge e,so that any path of length 3 have 3 different colors.By the definition of edge coloring,strong edge coloring and list strong edge coloring,we haveχ’（G）≤χ_s’（G）≤χ_sl’（G）.Strong edge coloring was first defined by Fouquet and Jolivet,then in 1985,Erdos and Nesetril[8]proposed a conjecture about strong edge coloring:The case when Δ≤3 has been proved.There are few results about the case when Δ≥4.In 1993,Brualdi and Massey[3]proposed another conjecture about strong edge col-oring:If G is a（a,b）-bipartite graph,then χ’s≤ab.The case when a=3 has been proved.There are also few results about the case when Δ≥4.None result about the list version of the conjecture.In this paper,we proved that planar graphs with maximum degree 4 has χ_sl’（G）≤19.This result partly conformed the conjecture proposed by Erdos and Nesetril.In Chapter 1,B ackground,Definition,Main tools and methods,Main result.In Chapter 2,Forbidden constructions,Discharging.In Chapter 3,Conclusion.