The Linear Arboricity of the Schrijver Graph SG(2k+2,k)

The linear arboricity la(G) of a graph G is the minimum number of linear forestswhich partition the edge set E(G) of G. The vertex linear arboricity vla(G) of a graph G isthe minimum number of subsets into which the vertex set V(G) can be partitioned so thatevery subset induces a linear forest. The Schrijver graph SG(n;k) is the graph whose vertexset consists of all 2-stable k-subsets of the set [n] = { 0,1, ... ,n}1g and two vertices A andB are adjacent if and only if A∩B =ɸ. In this paper, it is proved that la(SG(2k+2,k)) =[(k+2)/2] for k ≥ 3 and vla(SG(2k+2,k)) = va(SG(2k+2,k)) = 2 for k ≥ 2.