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Discussiones Mathematicae Graph Theory 29(1) (2009) 199-202
DOI: https://doi.org/10.7151/dmgt.1440

A NOTE ON k-UNIFORM SELF-COMPLEMENTARY HYPERGRAPHS OF GIVEN ORDER

Artur Szymański  and  A. Paweł Wojda

Faculty of Applied Mathematics
AGH University of Science and Technology
Al. Mickiewicza 30, 30-053 Kraków, Poland
e-mail: szymansk@agh.edu.pl, wojda@agh.edu.pl

Abstract

We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if (n || k) is even.

Keywords: self-complementing permutation, self-complementary hypergraph, k-uniform hypergraph, binomial coefficients.

2000 Mathematics Subject Classification: 05C65.

References

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[6]	A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Math. 25/2 (2005) 319-323.
[7]	A.P. Wojda, Self-complementary hypergraphs, Discuss. Math. Graph Theory 26 (2006) 217-224, doi: 10.7151/dmgt.1314.

Received 16 October 2007
Revised 1 December 2008
Accepted 1 December 2008