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 to 3 modulo 4, and it is proved that there exist a quasi regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent to 3 modulo 4.
@article{bwmeta1.element.doi-10_7151_dmgt_1919,
author = {Lata N. Kamble and Charusheela M. Deshpande and Bhagyashree Y. Bam},
title = {Almost Self-Complementary 3-Uniform Hypergraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {131-140},
zbl = {1354.05098},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1919}
}
Lata N. Kamble; Charusheela M. Deshpande; Bhagyashree Y. Bam. Almost Self-Complementary 3-Uniform Hypergraphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 131-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1919/