不含相交6-圈的曲面图的列表单射染色

List Injective Coloring of Embedded Graphs with No Intersecing 6-cycles

图G的一个点染色称为单射染色,如果任何两个有公共邻点的顶点染不同的颜色·一个图G称为单射κ-可选择的,如果对于顶点V(G)的任何一个大小为κ的允许颜色列表L,都存在一个单射染色φ,使得对于v∈V(G),有φ(v)∈L(v)使得G为单射κ-可选择的最小κ,称为G的单射可选择数,记作X_i^l(G).设G是最大度为Δ,围长为g的可嵌入到欧拉示性数X(∑)≥0的曲面∑的一个图,证明了若Δ≥7,g≥6,且不含有相交6-圈,则x_i^l(G)≤Δ+2.

A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors.A graph G is injectively k-choosable if any list L of admissible colors on V（G） of size k allows an injective coloring ψ such that ψ（v） ∈ L（v） whenever v ∈ V（G）.The least k for which G is injectively k-choosable is denoted by xli（G）.In this paper,we prove that if G is a graph embedded in a surface E of Euler characteristic x（∑） ≥ 0 with maximum degree △ and girth g,xli（G） ≤ △ ＋ 2 if △ ≥ 7,g ≥ 6 and G has no intersecting 6-cycles.