Halin图的集染色

The Set Coloring of Halin Graphs

对于非平凡连通图G,G的k集染色是指映射c:V(G)→Nk,对任意顶点v∈V(G),定义邻色集cN(v)={c(u)|u∈N(v)},若对uv∈E(G)有cN(u)≠cN(v),则称c为G的一个k集染色.满足上述条件的最小k值称为G的集色数,记为χs(G).为了更快更有效地给Halin图着色,采用集染色的着色方法,证明了当p≥4时,Halin图G(Cp,Tq)的集色数是3,并且还证明了对任意的Halin图G(Cp,Tq),有p+1≤q≤2p-2成立.

For a non - trivial connected graph G, let c： V（G）---＋Nk be a vertex coloring of G where adjacent vertices may be col- ored the same. For a vertex v of G , the neighborhood color set cN（v） is the set of colors of the neighbors ofv. The coloring c is called a k set coloring if cN（u） #cN（v） for every pair u, v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number,x, （G） of G. It is proved that the set chromatic number of the Halin graph G（ Co, Tq ） with p 34 is 3, and that for any a Halin graph G（ Co, T ）, there exists p ＋ 1 q 〈2p - 2.