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The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs

Lata N. Kamble;  Charusheela M. Deshpande;  Bhagyashree Y. Bam — 2016

Discussiones Mathematicae Graph Theory

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...

Almost Self-Complementary 3-Uniform Hypergraphs

Lata N. Kamble;  Charusheela M. Deshpande;  Bhagyashree Y. Bam — 2017

Discussiones Mathematicae Graph Theory

It is known that self-complementary 3-uniform hypergraphs on n vertices exist if and only if n is congruent to 0, 1 or 2 modulo 4. In this paper we define an almost self-complementary 3-uniform hypergraph on n vertices and prove that it exists if and only if n is congruent to 3 modulo 4. The structure of corresponding complementing permutation is also analyzed. Further, we prove that there does not exist a regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent...

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