Geodesic
The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 419-426

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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.
Keywords: self-complementary hypergraph, uniform hypergraph, regular hypergraph, quasi regular hypergraph, bi-regular hypergraph 
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Kamble, Lata N.; Deshpande, Charusheela M.; Bam, Bhagyashree Y. The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 419-426. http://geodesic.mathdoc.fr/item/DMGT_2016_36_2_a12/