Self-complementary hypergraphs

• Autorzy: A. Paweł Wojda
• Języki publikacji: EN

Abstrakty

EN

A k-uniform hypergraph H = (V;E) is called self-complementary if there is a permutation σ:V → V, called self-complementing, 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 $H' = (V; \binom{V}{k} - E)$.
In the present paper, for every k, (1 ≤ k ≤ n), we give a characterization of self-complementig permutations of k-uniform self-complementary hypergraphs of the order n. This characterization implies the well known results for self-complementing permutations of graphs, given independently in the years 1962-1963 by Sachs and Ringel, and those obtained for 3-uniform hypergraphs by Kocay, for 4-uniform hypergraphs by Szymański, and for general (not uniform) hypergraphs by Zwonek.

Słowa kluczowe

EN

k-uniform hypergraph; self-complementary hypergraph

Kategorie tematyczne

• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 217-224

Daty

wydano

2006

otrzymano

2005-07-18

poprawiono

2006-02-04

Twórcy

autor

A. Paweł Wojda

• AGH University of Science and Technology, Faculty of Applied Mathematics, Department of Discrete Mathematics, Al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] A. Benhocine and A.P. Wojda, On self-complementation, J. Graph Theory 8 (1985) 335-341, doi: 10.1002/jgt.3190090305.
• [2] W. Kocay, Reconstructing graphs as subsumed graphs of hypergraphs, and some self-complementary triple systems, Graphs and Combinatorics 8 (1992) 259-276, doi: 10.1007/BF02349963.
• [3] G. Ringel, Selbstkomplementäre Graphen, Arch. Math. 14 (1963) 354-358, doi: 10.1007/BF01234967.
• [4] H. Sachs, Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962) 270-288.
• [5] A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Mathematica 25/2 (2005) 319-323.
• [6] M. Zwonek, A note on self-complementary hypergraphs, Opuscula Mathematica 25/2 (2005) 351-354.

Identyfikatory

DOI

10.7151/dmgt.1314