Generating self-complementary uniform hypergraphs

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Generating self-complementary uniform hypergraphs

Show simple item record Gosselin, Shonda 2010-12-17T20:31:04Z 2010-12-17T20:31:04Z 2010-02
dc.description.abstract In 2007, Szymanski and Wojda proved that for positive integers n; k with k<n, a self-complementary k-uniform hypergraph of order n exists if and only if n/k is even. In this paper, we characterize the cycle type of a k-complementing permutation in Sym.n/ which has order equal to a power of 2. This yields a test for determining whether a finite permutation is a k-complementing permutation, and an algorithm for generating all self-complementary k-hypergraphs of order n, up to isomorphism, for feasible n.We also obtain an alternative description of the necessary and sufficient conditions on the order of a self-complementary k-uniform hypergraph, in terms of the binary representation of k. This extends previous results for the cases k D 2; 3; 4 due to Ringel, Sachs, Suprunenko, Kocay and Szymanski. en_US
dc.description.sponsorship University of Winnipeg en_US
dc.language.iso en en_US
dc.publisher Discrete Mathematics en_US
dc.subject Self-complementary graphs en_US
dc.subject Uniform hypergraphs en_US
dc.subject Complementing permutation en_US
dc.title Generating self-complementary uniform hypergraphs en_US
dc.type Article en_US

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