Self-complementary hypergraphs

A. 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 -