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

Abstract

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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.

How to cite

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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 -

References

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  6. [6] P. Potočnik and M. Šajana, The existence of regular self-complementary 3-uniform hypergraphs, Discrete Math. 309 (2009) 950-954. doi:10.1016/j.disc.2008.01.026[Crossref][WoS] 
  7. [7] G. Ringel, Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354-358. doi:10.1007/BF01234967[Crossref] 
  8. [8] H. Sachs, Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270-288. Zbl0119.18904
  9. [9] A. Szymański and A.P.Wojda, A note on k-uniform self-complementary hypergraphs of given order, Discuss. Math. Graph Theory 29 (2009) 199-202. doi:10.7151/dmgt.1440[Crossref] Zbl1189.05119

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