Geodesic
Almost Self-Complementary Uniform Hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 607-610.

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A k-uniform hypergraph (k-hypergraph) is almost self-complementary if it is isomorphic with its complement in the complete k-uniform hypergraph minus one edge. We prove that an almost self-complementary k-hypergraph of order n exists if and only if nk is odd.
Keywords: uniform hypergraph 
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Wojda, Adam Paweł. Almost Self-Complementary Uniform Hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 607-610. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a18/

[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] J.W.L. Glaisher, On the residue of a binomial coefficient with respect to a prime modulus, Quart. J. Math. 30 (1899) 150–156.

[3] L.N. Kamble, C.M. Deshpande and B.Y. Bam, Almost self-complementary 3- uniform hypergraphs, Discuss. Math. Graph Theory 37 (2017) 131–140. doi:10.7151/dmgt.1919

[4] S.H. Kimball, T.R. Hatcher, J.A. Riley and L. Moser, Solution to problem E 1288 : Odd binomial coefficients, Amer. Math. Monthly 65 (1958) 368–369. doi:10.2307/2308812

[5] E.E. Kummer, Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew. Math. 44 (1852) 93–146. doi:10.1515/crll.1852.44.93

[6] E. Lucas, Sur les congruences des nombres eulériens st des coefficients differentiels, Bull. Soc. Math. France 6 (1878) 49–54. doi:10.24033/bsmf.127

[7] G. Ringenboim, Fermat’s Last Theorem for Amateurs (Springer Verlag, 1999).

[8] 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

[9] A.P. Wojda, Self-complementary hypergraphs, Discuss. Math. Graph Theory 26 (2006) 217–224. doi:/10.7151/dmgt.1314