A note on k-uniform self-complementary hypergraphs of given order

• Autorzy: Artur Szymański , A. Paweł Wojda
• Języki publikacji: EN

Abstrakty

EN

We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if $\binom{n}{k}$ is even.

Słowa kluczowe

EN

self-complementing permutation; self-complementary hypergraph; k-uniform hypergraph; binomial coefficients

Kategorie tematyczne

• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 1
• Strony: 199-202

Daty

wydano

2009

otrzymano

2007-10-16

poprawiono

2008-12-01

zaakceptowano

2008-12-01

Twórcy

autor

Artur Szymański

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-053 Kraków, Poland

autor

A. Paweł Wojda

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-053 Kraków, Poland

Bibliografia

• [1] J.W.L. Glaisher, On the residue of a binomial coefficient with respect to a prime modulus, Quarterly Journal of Mathematics 30 (1899) 150-156.
• [2] S.H. Kimball, T.R. Hatcher, J.A. Riley and L. Moser, Solution to problem E1288: Odd binomial coefficients, Amer. Math. Monthly 65 (1958) 368-369, doi: 10.2307/2308812.
• [3] 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.
• [4] G. Ringel, Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354-358, doi: 10.1007/BF01234967.
• [5] H. Sachs, Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270-288.
• [6] A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Math. 25/2 (2005) 319-323.
• [7] A.P. Wojda, Self-complementary hypergraphs, Discuss. Math. Graph Theory 26 (2006) 217-224, doi: 10.7151/dmgt.1314.

Identyfikatory

DOI

10.7151/dmgt.1440