TY  - JOUR
ID  - Szymański2005
LB  - Szymański2005
AU  - Szymański, Artur
TI  - A note on self-complementary 4-uniform hypergraphs
ST  - A note on self-complementary 4-uniform hypergraphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2005
VL  - 25
IS  - 2
SP  - 319
EP  - 323
DO  - http://dx.doi.org/10.7494/OpMath.2005.25.2.319
UR  - http://dx.doi.org/10.7494/OpMath.2005.25.2.319
AB  - We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\) or \(3\) fixed points, and all other cycles have length a multiple of \(8\), (iii) \(\theta\) has \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (iv) \(\theta\) has \(1\) fixed point, \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (v) \(\theta\) has \(1\) cycle of length \(3\), and all other cycles have length a multiple of \(8\). Moreover, we present algorithms for generating every possible \(3\) and \(4\)-uniform self-complementary hypergraphs.
KW  - complementing permutation
KW  - self-complementary hypergraph
KW  - \(k\)-uniform hypergraph
SN  - 1232-9274
ER  -