Geodesic
Almost Self-Complementary 3-Uniform Hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 131-140.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: uniform hypergraph, self-complementary hypergraph, almost complete 3-uniform hypergraph, almost self-complementary hypergraph, quasi regular hypergraph 
@article{DMGT_2017_37_1_a9,
     author = {Kamble, Lata N. and Deshpande, Charusheela M. and Bam, Bhagyashree Y.},
     title = {Almost {Self-Complementary} {3-Uniform} {Hypergraphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {131--140},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a9/}
}
TY  - JOUR
AU  - Kamble, Lata N.
AU  - Deshpande, Charusheela M.
AU  - Bam, Bhagyashree Y.
TI  - Almost Self-Complementary 3-Uniform Hypergraphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 131
EP  - 140
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a9/
LA  - en
ID  - DMGT_2017_37_1_a9
ER  - 
%0 Journal Article
%A Kamble, Lata N.
%A Deshpande, Charusheela M.
%A Bam, Bhagyashree Y.
%T Almost Self-Complementary 3-Uniform Hypergraphs
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 131-140
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a9/
%G en
%F DMGT_2017_37_1_a9
Kamble, Lata N.; Deshpande, Charusheela M.; Bam, Bhagyashree Y. Almost Self-Complementary 3-Uniform Hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 131-140. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a9/

[1] C.R.J. Clapham, Graphs self-complementary in Kn-e, Discrete Math. 81 (1990) 229–235. doi:10.1016/0012-365X(90)90062-M

[2] C.J. Colbourn and J.H. Dinitz, The CRC Handbook of Combinatorial Designs (CRC Press, Boca Raton, 1996).

[3] P.K. Das, Almost self-complementary graphs 1, Ars Combin. 31 (1991) 267–276.

[4] P.K. Das and A. Rosa, Halving Steiner triple systems, Discrete Math. 109 (1992) 59–67. doi:10.1016/0012-365X(92)90278-N

[5] S. Gosselin, Constructing regular self-complementary uniform hypergraphs, Combin. Designs 16 (2011) 439–454. doi:10.1002/jcd.20286

[6] A. Hartman, Halving the complete design, Ann. Discrete Math. 34 (1987) 207–224. doi:10.1016/s0304-0208(08)72888-3

[7] L.N. Kamble, C.M. Deshpande and B.Y. Bam, The existence of quasi regular and bi-regular self-complementary 3 -uniform hypergraphs, Discuss. Math. Graph Theory 36 (2016) 419–426. doi:10.7151/dmgt.1862

[8] M. Knor and P. Potočnik, A note on 2 -subset-regular self-complementary 3 -uniform hypergraphs, Ars Combin. 11 (2013) 33–36.

[9] W. Kocay, Reconstructing graphs as subsumed graphs of hypergraphs, and some self-complementary triple systems, Graphs Combin. 8 (1992) 259–276. doi:10.1007/BF02349963

[10] 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

[11] G. Ringel, Über Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354–358. doi:10.1007/BF01234967

[12] H. Sachs, Über Selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270–288.

[13] 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