Abstract
Let Dn,k be the set of all permutations of the symmetric group Sn that have no cycles of length i for all 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,Dn,k) is equal to the set of all the largest independent sets in the derangement graph Cay(Sn,Dn,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.
Original language | English |
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Pages (from-to) | 575-579 |
Number of pages | 5 |
Journal | Journal of Algebraic Combinatorics |
Volume | 59 |
Issue number | 3 |
DOIs | |
State | Published - May 2024 |
Keywords
- Alternating group
- Cayley graphs
- Derangements
- Erdos–Ko–Rado combinatorics
- Representation theory
- Symmetric group
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics