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.
@article{bwmeta1.element.doi-10_7151_dmgt_1862,
author = {Lata N. Kamble and Charusheela M. Deshpande and Bhagyashree Y. Bam},
title = {The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {419-426},
zbl = {1338.05191},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1862}
}
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) pp. 419-426. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1862/