$S_{5}$-DECOMPOSITION OF KNESER GRAPHS

Let $A = \{1,2,3,...,n\}$ and $\mathcal P_{k}(A)$ denotes the set of all $k$-element subsets of $A$. The Kneser graph $KG_{n,2}$ has the vertex set $V(KG_{n,2})$= $\mathcal P_{2}(A)$ and edge set $E(KG_{n,2})=\{XY|X,Y\in \mathcal{P}_{2}(A)$ and $X\cap Y=\emptyset\}$. A star with $k$ edges is denoted by $S_{k}$. In this paper, we show that the graph $KG_{n,2}$ can be decomposed into $S_{5}$ if and only if $n\geq 7$ and $n\equiv 0,1,2,3(mod\ 5)$.