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

Artur Szymański; A. Paweł Wojda

Discussiones Mathematicae Graph Theory (2009)

  • Volume: 29, Issue: 1, page 199-202
  • ISSN: 2083-5892

Abstract

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

How to cite

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Artur Szymański, and A. Paweł Wojda. "A note on k-uniform self-complementary hypergraphs of given order." Discussiones Mathematicae Graph Theory 29.1 (2009): 199-202. <http://eudml.org/doc/270314>.

@article{ArturSzymański2009,
abstract = {We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if $\binom\{n\}\{k\}$ is even.},
author = {Artur Szymański, A. Paweł Wojda},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {self-complementing permutation; self-complementary hypergraph; k-uniform hypergraph; binomial coefficients; -uniform hypergraph},
language = {eng},
number = {1},
pages = {199-202},
title = {A note on k-uniform self-complementary hypergraphs of given order},
url = {http://eudml.org/doc/270314},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Artur Szymański
AU - A. Paweł Wojda
TI - A note on k-uniform self-complementary hypergraphs of given order
JO - Discussiones Mathematicae Graph Theory
PY - 2009
VL - 29
IS - 1
SP - 199
EP - 202
AB - We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if $\binom{n}{k}$ is even.
LA - eng
KW - self-complementing permutation; self-complementary hypergraph; k-uniform hypergraph; binomial coefficients; -uniform hypergraph
UR - http://eudml.org/doc/270314
ER -

References

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  1. [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. Zbl29.0152.03
  2. [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. [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. Zbl0759.05064
  4. [4] G. Ringel, Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354-358, doi: 10.1007/BF01234967. 
  5. [5] H. Sachs, Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270-288. Zbl0119.18904
  6. [6] A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Math. 25/2 (2005) 319-323. Zbl1122.05067
  7. [7] A.P. Wojda, Self-complementary hypergraphs, Discuss. Math. Graph Theory 26 (2006) 217-224, doi: 10.7151/dmgt.1314. Zbl1142.05058

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