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Abstract Let D₍, ₊ D n, k be the set of all permutations of the symmetric group Sₙ S n that have no cycles of length i for all 1 i k 1 ≤ i ≤ k. In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph Cay (Sₙ, D₍, ₊) Cay (S n, D n, k) is equal to the set of all the largest independent sets in the derangement graph Cay (Sₙ, D₍, ₁) Cay (S n, D n, 1), provided n is sufficiently large in terms of k. We give a simpler proof that holds for all n, k and also applies to the alternating group.
Filmus et al. (Fri,) studied this question.