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.
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