Halin图的边列表染色

ON EDGE LIST COLORING OF THE HALIN-GRAPHS

Halin图是3－连通平面图，且存在一个面，去掉与该面关联的边后是一棵树。图的边列表染色是任给图G的每条边e配一颜色集合L（e），满足｜L（e）｜=k，k为某确定整数，G的每条边若均可着从L（e）中选择出的一种颜色，使得任一关联的边对着色不同，则称G是k一边可选择的，min（k）称为G的边选择数或边列表色数，记（G）。本文对Halin图证明了列表染色猜想在Δ≠3时成立。即xL=x。

A Halin graph G is a 3-Connected planar graph with a face f such that G - E(f) is a tree, The edge list chromatic number of a graph G, denoted by X.(G), is the minimum number k such that if we give lists of k colors to each edge of G, there is a edge coloring of g, Where each edge receives a color from its own list no matter what the lists are. In this paper, we prove the 'List Coloring Conjecture' for Halin graphs with Δ≠3, i.e. XL(G) = X-(G).