English

Properties of Generalized Derangement Graphs

Combinatorics 2011-06-29 v1

Abstract

A permutation sigma in Sn is a k-derangement if for any subset X = {a1, . . ., ak} \subseteq [n], {sigma(a1), . . ., sigma(ak)} is not equal to X. One can form the k-derangement graph on the set of permutations of Sn by connecting two permutations sigma and tau if sigma(tau)^-1 is a k-derangement. We characterize when such a graph is connected or Eulerian. For n an odd prime power, we determine the independence, clique and chromatic number of the 2-derangement graph.

Keywords

Cite

@article{arxiv.1106.5522,
  title  = {Properties of Generalized Derangement Graphs},
  author = {Hannah Jackson and Kathryn Nyman and Les Reid},
  journal= {arXiv preprint arXiv:1106.5522},
  year   = {2011}
}

Comments

8 pages, 1 figure

R2 v1 2026-06-21T18:28:20.877Z