Almost t-complementary uniform hypergraphs

Abstract

An almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation \(\theta \in Sym(V)\) such that the sets \(E, E^\theta , E^{\theta ^2}, \ldots , E^{\theta ^{t-1}}\) partition the set of all k-subsets of V minus one edge. Such a permutation \(\theta \) is called an almost (t, k)-complementing permutation. Almost t-complementary k-hypergraphs are a natural generalization of almost self-complementary graphs, which were previously studied by Clapham, Kamble et al., and Wojda. We prove that there exists an almost p-complementary k-hypergraph of order n whenever the base-p representation of k is a subsequence of the base-p representation of n, where p is prime.

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Correspondence to Shonda Gosselin.

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Gosselin, S. Almost t-complementary uniform hypergraphs. Aequat. Math. 93, 1177–1182 (2019). https://doi.org/10.1007/s00010-018-0631-y

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Mathematics Subject Classification

  • 05C65
  • 05E20
  • 05C25
  • 05C85

Keywords

  • Almost self-complementary hypergraph
  • Uniform hypergraph
  • Almost (t, k)-complementing permutation