Hamiltonicity of Schrijver graphs and stable Kneser graphs
CoRR(2024)
摘要
For integers k≥ 1 and n≥ 2k+1, the Schrijver graph S(n,k) has as
vertices all k-element subsets of [n]:={1,2,…,n} that contain no two
cyclically adjacent elements, and an edge between any two disjoint sets. More
generally, for integers k≥ 1, s≥ 2, and n ≥ sk+1, the s-stable
Kneser graph S(n,k,s) has as vertices all k-element subsets of [n] in
which any two elements are in cyclical distance at least s. We prove that all
the graphs S(n,k,s), in particular Schrijver graphs S(n,k)=S(n,k,2), admit
a Hamilton cycle that can be computed in time 𝒪(n) per generated
vertex.
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