Cyclically t-complementary uniform hypergraphs

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Cyclically t-complementary uniform hypergraphs

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dc.contributor.author Gosselin, Shonda
dc.date.accessioned 2010-12-17T20:16:46Z
dc.date.available 2010-12-17T20:16:46Z
dc.date.issued 2010-05
dc.identifier.uri http://hdl.handle.net/10680/293
dc.description.abstract A cyclically t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation 2 Sym.V/ such that the sets E; E ; E 2; : : : ; E t􀀀1 partition the set of all k-subsets of V. Such a permutation is called a .t; k/-complementing permutation. The cyclically t-complementary k-hypergraphs are a natural and useful generalization of the self-complementary graphs, which have been studied extensively in the past due to their important connection to the graph isomorphism problem. For a prime p, we characterize the cycle type of the .pr ; k/- complementing permutations 2 Sym.V/ which have order a power of p. This yields a test for determining whether a permutation in Sym.V/ is a .pr ; k/-complementing permutation, and an algorithm for generating all of the cyclically pr-complementing k- hypergraphs of order n, for feasible n, up to isomorphism. We also obtain some necessary and sufficient conditions on the order of these structures. This generalizes previous results due to Ringel, Sachs, Adamus, Orchel, Szyma«ski, Wojda, Zwonek, and Bernaldez. en_US
dc.description.sponsorship University of Winnipeg en_US
dc.language.iso en en_US
dc.publisher European Journal of Combinatorics en_US
dc.subject Hypergraphs en_US
dc.subject Self-complementary graphs en_US
dc.title Cyclically t-complementary uniform hypergraphs en_US
dc.type Article en_US

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