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Almost t-complementary uniform hypergraphs

  • Shonda GosselinEmail author
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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.

Keywords

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

Mathematics Subject Classification

05C65 05E20 05C25 05C85 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of WinnipegWinnipegCanada

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