# Self-complementary hypergraphs

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 2, page 217-224
- ISSN: 2083-5892

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topA. Paweł Wojda. "Self-complementary hypergraphs." Discussiones Mathematicae Graph Theory 26.2 (2006): 217-224. <http://eudml.org/doc/270729>.

@article{A2006,

abstract = {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 $H^\{\prime \} = (V; \binom\{V\}\{k\} - E)$.
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.},

author = {A. Paweł Wojda},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {k-uniform hypergraph; self-complementary hypergraph; -uniform hypergraph},

language = {eng},

number = {2},

pages = {217-224},

title = {Self-complementary hypergraphs},

url = {http://eudml.org/doc/270729},

volume = {26},

year = {2006},

}

TY - JOUR

AU - A. Paweł Wojda

TI - Self-complementary hypergraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 2

SP - 217

EP - 224

AB - 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 $H^{\prime } = (V; \binom{V}{k} - E)$.
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.

LA - eng

KW - k-uniform hypergraph; self-complementary hypergraph; -uniform hypergraph

UR - http://eudml.org/doc/270729

ER -

## References

top- [1] A. Benhocine and A.P. Wojda, On self-complementation, J. Graph Theory 8 (1985) 335-341, doi: 10.1002/jgt.3190090305. Zbl0587.05054
- [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. Zbl0759.05064
- [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. Zbl0119.18904
- [5] A. Szymański, A note on self-complementary 4-uniform hypergraphs, Opuscula Mathematica 25/2 (2005) 319-323. Zbl1122.05067
- [6] M. Zwonek, A note on self-complementary hypergraphs, Opuscula Mathematica 25/2 (2005) 351-354. Zbl1122.05068

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