The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, Tome 36 (2016) no. 2, p. 419.

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A k-uniform hypergraph H = (V ;E) is called self-complementary if there is a permutation σ : V → V , called a complementing permutation, such that for every k-subset e of V , e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H′ = (V ; V(k) − E). In this paper we define a bi-regular hypergraph and prove that there exists a bi-regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 or 2 modulo 4. We also prove that there exists a quasi regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 modulo 4.
Classification : 05C65
Mots-clés : self-complementary hypergraph, uniform hypergraph, regular hypergraph, quasi regular hypergraph, bi-regular hypergraph 
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Lata N. Kamble; Charusheela M. Deshpande; Bhagyashree Y. Bam. The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) no. 2, p. 419. https://geodesic-test.mathdoc.fr/item/DMGT_2016__36_2_277125/