整数距离图G(D_(m,2))的点线性荫度

The vertex linear arboricity of the integer distance graph G(D_(m,2))

整数距离图G(D)以全体整数为顶点集 ,顶点u ,v相邻当且仅当 |u -v|∈D ,其中D是一个正整数集 .对于m 11,设Dm ,2 ={ 1,2 ,… ,m} \{ 2 } ,得到了G(Dm ,2 )的点线性荫度的上界和下界并决定出了它在某些特殊的m上的确切值 .

An integer distance graph is a graph G(D) with the set of all integers Z as vertex set and two vertices u,v∈Z are adjacent if and only if |u-v|∈D where the distance set D is a subset of positive integers. Let D m,2=｛1,2,…,m｝\｛2｝ for m11. In this paper, an upper bound and a lower bound of the vertex linear arboricity of G(D m,2) are obtained and the exact values of it is determined for some special values m.