Temat: k-uniform hypergraph - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A note on self-complementary 4-uniform hypergraphs
Autorzy:: Szymański, A.
Powiązania:: https://bibliotekanauki.pl/articles/255191.pdf
Data publikacji:: 2005
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: complementing permutation
self-complementary hypergraph
k-uniform hypergraph
Opis:: 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 hypergraph.
Źródło:: Opuscula Mathematica; 2005, 25, 2; 319-323
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Self-complementary hypergraphs
Autorzy:: Wojda, A.
Powiązania:: https://bibliotekanauki.pl/articles/743928.pdf
Data publikacji:: 2006
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: k-uniform hypergraph
self-complementary hypergraph
Opis:: 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.
Źródło:: Discussiones Mathematicae Graph Theory; 2006, 26, 2; 217-224
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: A note on k-uniform self-complementary hypergraphs of given order
Autorzy:: Szymański, Artur
Wojda, A.
Powiązania:: https://bibliotekanauki.pl/articles/743151.pdf
Data publikacji:: 2009
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: self-complementing permutation
self-complementary hypergraph
k-uniform hypergraph
binomial coefficients
Opis:: We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if $\binom{n}{k}$ is even.
Źródło:: Discussiones Mathematicae Graph Theory; 2009, 29, 1; 199-202
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Cyclic Partitions of Complete and Almost Complete Uniform Hypergraphs
Autorzy:: Dilbarjot
Gosselin, Shonda Dueck
Powiązania:: https://bibliotekanauki.pl/articles/32305661.pdf
Data publikacji:: 2022-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: almost self-complementary hypergraph
uniform hypergraph
cyclically t -complementary hypergraph
( t,k )-complementing permutation
Opis:: We consider cyclic partitions of the complete $k$-uniform hypergraph on a finite set $V$, minus a set of $s$ edges, $ s \ge 0 $. An $s$-almost $t$-complementary $k$-hypergraph is a $k$-uniform hypergraph with vertex set $V$ and edge set $E$ for which there exists a permutation $ \theta \in Sym(V)$ such that the sets $E$, $ E^\theta $, $ E^\{\theta^2} $, . . ., $ E^{\theta^{t−1}} $ partition the set of all $k$-subsets of $V$ minus a set of $s$ edges. Such a permutation $ \theta $ is called an $s$-almost $(t, k)$-complementing permutation. The $s$-almost $t$-complementary $k$-hypergraphs are a natural generalization of the almost self-complementary graphs which were previously studied by Clapham, Kamble et al. and Wojda. We prove the existence of an $s$-almost $ p^\alpha $-complementary $k$-hypergraph of order $n$, where $p$ is prime, $ s= \Pi_{i \ge 0 } \binom{n_i}{k_i} $, and $n_i$ and $k_i$ are the entries in the base-$ p^\alpha $ representations of $n$ and $k$, respectively. This existence result yields a combinatorial argument which generalizes Lucas’ classic 1878 number theory result to prime powers, which was originally proved by Davis and Webb in 1990 by another method. In addition, we prove an alternative statement of the necessary and sufficient conditions for the existence of a $ p^\alpha $-complementary $k$-hypergraph, and the equivalence of these two conditions yield an interesting relationship between the base-$p$ representation and the base-$ p^\alpha $ representation of a positive integer $n$. Finally, we determine a set of necessary and sufficient conditions on $n$ for the existence of a $t$-complementary $k$-uniform hypergraph on $n$ vertices for composite values of $t$, extending previous results due to Wojda, Szymański and Gosselin.
Źródło:: Discussiones Mathematicae Graph Theory; 2022, 42, 3; 747-758
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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