This article demonstrates that connected s-stable kneser graphs are Hamiltonian, indicating their structure supports cycles.
The Kneser Graph $K(n,k)$ has as vertices all k-subsets of \1,…,n\ and edges connecting two vertices if they are disjoint. The s-stable Kneser Graph Ks-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.
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Ledezma et al. (2025) studied this question.
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