Opuscula Math. 25, no. 2 (2005), 351-354

Opuscula Mathematica

# A note on self-complementary hypergraphs

Małgorzata Zwonek

Abstract. In the paper we describe all self-complementary hypergraphs. It turns out that such hypergraphs exist if and only if the number of vertices of the hypergraph is of the form $$n=2^k$$. This answers a conjecture posed by A. Szymański (see [Szymański A.: Note on self-complementary 4-uniform hypergraphs.(Preprint)]).

Keywords: self-complementary hypergraphs, complementing permutation.

Mathematics Subject Classification: 05C65.

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