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

Lata N. Kamble, Charusheela M. Deshpande, and Bhagyashree Y. Bam. "The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 419-426. <http://eudml.org/doc/277125>.

@article{LataN2016,
abstract = {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.},
author = {Lata N. Kamble, Charusheela M. Deshpande, Bhagyashree Y. Bam},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {self-complementary hypergraph; uniform hypergraph; regular hypergraph; quasi regular hypergraph; bi-regular hypergraph},
language = {eng},
number = {2},
pages = {419-426},
title = {The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs},
url = {http://eudml.org/doc/277125},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Lata N. Kamble
AU - Charusheela M. Deshpande
AU - Bhagyashree Y. Bam
TI - The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 419
EP - 426
AB - 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.
LA - eng
KW - self-complementary hypergraph; uniform hypergraph; regular hypergraph; quasi regular hypergraph; bi-regular hypergraph
UR - http://eudml.org/doc/277125
ER -