Properties of Generalized Derangement Graphs
Abstract
A permutation sigma in Sn is a k-derangement if for any subset X = a1, . . ., ak ⊂eq [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.
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