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

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

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 2, page 419-426
- ISSN: 2083-5892

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topLata 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 -

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