$s$-Stable Kneser Graph are Hamiltonian

Abstract

The Kneser Graph $K(n,k)$ has as vertices all $k$-subsets of $\{1,\ldots,n\}$ and edges connecting two vertices if they are disjoint. The $s$-stable Kneser Graph $K_{s-\text{stab}}(n, k)$ is obtained from the Kneser graph by deleting vertices with elements at cyclic distance less than $s$. In this article, we show that connected $s$-Stable Kneser graphs are Hamiltonian.