S5-Decomposition of Kneser Graphs

Let A = {1, 2, 3, ..., n} and Pk(A) denotes the set of all k-element subsets of A. The Kneser graph KGn,2 has the vertex set V (KGn,2)= P2(A) and edge set E(KGn,2) = {XY |X, Y ∈ P2(A) and X ∩ Y = ∅}. A star with k edges is denoted by Sk. In this paper, we show that the graph KGn,2 can be decomposed into S5 if and only if n ≥ 7 and n ≡ 0, 1, 2, 3(mod 5).