Browsing by Subject "complementing permutation"

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Access status: Open Access ,
A note on self-complementary 4-uniform hypergraphs
(2005) Szymański, Artur
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.
Access status: Open Access ,
A note on self-complementary hypergraphs
(2005) Zwonek, Małgorzata
In the paper we desribe all self-complementary hypergraphs. It turns out that such hypergraphs exist if and only if the number of vertices of the hypergraph is of the form $n=2^k$. This answers a conjecture posed by A. Szymański (see [3]).