Almost Self-Complementary 3-Uniform Hypergraphs

Lata N. Kamble, Charusheela M. Deshpande, and Bhagyashree Y. Bam. "Almost Self-Complementary 3-Uniform Hypergraphs." Discussiones Mathematicae Graph Theory 37.1 (2017): 131-140. <http://eudml.org/doc/288081>.

@article{LataN2017,
abstract = {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.},
author = {Lata N. Kamble, Charusheela M. Deshpande, Bhagyashree Y. Bam},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {uniform hypergraph; self-complementary hypergraph; almost complete 3-uniform hypergraph; almost self-complementary hypergraph; quasi regular hypergraph},
language = {eng},
number = {1},
pages = {131-140},
title = {Almost Self-Complementary 3-Uniform Hypergraphs},
url = {http://eudml.org/doc/288081},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Lata N. Kamble
AU - Charusheela M. Deshpande
AU - Bhagyashree Y. Bam
TI - Almost Self-Complementary 3-Uniform Hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 131
EP - 140
AB - 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.
LA - eng
KW - uniform hypergraph; self-complementary hypergraph; almost complete 3-uniform hypergraph; almost self-complementary hypergraph; quasi regular hypergraph
UR - http://eudml.org/doc/288081
ER -