Opuscula Mathematica

Opuscula Math.
 25
, no. 2
 (), 319-323
Opuscula Mathematica

A note on self-complementary 4-uniform hypergraphs


Abstract. We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\) or \(3\) fixed points, and all other cycles have length a multiple of \(8\), (iii) \(\theta\) has \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (iv) \(\theta\) has \(1\) fixed point, \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (v) \(\theta\) has \(1\) cycle of length \(3\), and all other cycles have length a multiple of \(8\). Moreover, we present algorithms for generating every possible \(3\) and \(4\)-uniform self-complementary hypergraphs.
Keywords: complementing permutation, self-complementary hypergraph, \(k\)-uniform hypergraph.
Mathematics Subject Classification: 34A30, 34B05, 35B12, 35A15, 35J50, 35J65, 46T15, 34B15.
Cite this article as:
Artur Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Math. 25, no. 2 (2005), 319-323
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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