$s$-Stable Kneser Graph are Hamiltonian

TL;DR

This paper proves that all connected $s$-stable Kneser graphs are Hamiltonian, extending the understanding of Hamiltonian cycles in these combinatorial structures.

Contribution

It establishes the Hamiltonicity of connected $s$-stable Kneser graphs, a significant extension of known properties of Kneser graphs.

Findings

Connected $s$-stable Kneser graphs are Hamiltonian.

Provides a new class of graphs with guaranteed Hamiltonian cycles.

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 $K_{s-stab}(n, k)$ 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 graph are Hamiltonian.