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Tytuł:
Almost Self-Complementary Uniform Hypergraphs
Autorzy:
Wojda, Adam Paweł
Powiązania:
https://bibliotekanauki.pl/articles/31342288.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
uniform hypergraph
Opis:
A $k$-uniform hypergraph ($k$-hypergraph) is almost self-complementary if it is isomorphic with its complement in the complete $k$-uniform hypergraph minus one edge. We prove that an almost self-complementary $k$-hypergraph of order $n$ exists if and only if \( \binom{n}{k} \) is odd.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 607-610
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decompositions of complete 3-uniform hypergraphs into cycles of constant prime length
Autorzy:
Lakshmi, R
Poovaragavan, T.
Powiązania:
https://bibliotekanauki.pl/articles/255686.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
uniform hypergraph
cycle decomposition
Opis:
A complete 3-unilorm hypergraph of order n has vertex set V with \V\ = n and the set ol all 3-subsets of V as its edge set. A t-cycle in this hypergraph is v1, e1, v2, e2,… , vt, et, v1 where v1, v2,…vt are distinct vertices and e1, e-2,..., et are distinct edges such that [formula] and [formula] A decomposition of a hypergraph is a partition of its edge set into edge-disjoint subsets. In this paper, we give necessary and sufficient conditions for a decomposition of the complete 3-unilorm hypergraph of order n into p-cycles, whenever p is prime.
Źródło:
Opuscula Mathematica; 2020, 40, 4; 509-516
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Subdivision of hypergraphs and their colorings
Autorzy:
Iradmusa, Moharram N.
Powiązania:
https://bibliotekanauki.pl/articles/255017.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
hypergraph
uniform hypergraph
subdivision of hypergraph
Opis:
In this paper we introduce the subdivision of hypergraphs, study their properties and parameters and investigate their weak and strong chromatic numbers in various cases.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 271-290
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The existence of bipartite almost self-complementary 3-uniform hypergraphs
Autorzy:
Kamble, L. N.
Deshpande, C. M.
Athawale, B. P.
Powiązania:
https://bibliotekanauki.pl/articles/29519545.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
almost self-complementary 3-uniform hypergraph
bipartite hypergraph
bipartite self-complementary 3-uniform hypergraph
bipartite almost self-complementary 3-uniform hypergraph
Opis:
An almost self-complementary 3-uniform hypergraph on n vertices exists if and only if n is congruent to 3 modulo 4. A hypergraph $ H $ with vertex set $ V $ and edge set $ E $ is called bipartite if $ V $ can be partitioned into two subsets $ V_1 $ and $ V_2 $ such that $ e ∩ V_1 ≠ ∅ $ and $e ∩ V_2 ≠ ∅ $ for any $ e ∈ E $. A bipartite self-complementary 3-uniform hypergraph $ H $ with partition $ (V_1, V_2) $ of the vertex set $ V $ such that $ |V_1| = m $ and $ |V_2| = n $ exists if and only if either (i) $ m = n $ or (ii) $ m ≠ n $ and either $ m $ or $ n $ is congruent to 0 modulo 4 or (iii) $ m ≠ n $ and both $ m $ and $ n $ are congruent to 1 or 2 modulo 4. In this paper we define a bipartite almost self-complementary 3-uniform hypergraph $ H $ with partition $ (V_1, V_2) $ of a vertex set $ V $ such that $ |V_1| = m $ and $ |V_2| = n $ and find the conditions on $ m $ and $ n $ for a bipartite 3-uniform hypergraph $ H $ to be almost self-complementary. We also prove the existence of bi-regular bipartite almost self-complementary 3-uniform hypergraphs.
Źródło:
Opuscula Mathematica; 2023, 43, 5; 663-673
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Tytuł:
Almost Self-Complementary 3-Uniform Hypergraphs
Autorzy:
Kamble, Lata N.
Deshpande, Charusheela M.
Bam, Bhagyashree Y.
Powiązania:
https://bibliotekanauki.pl/articles/31342164.pdf
Data publikacji:
2017-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
uniform hypergraph
self-complementary hypergraph
almost complete 3-uniform hypergraph
almost self-complementary hypergraph
quasi regular hypergraph
Opis:
It is known that self-complementary 3-uniform hypergraphs on n vertices exist if and only if n is congruent to 0, 1 or 2 modulo 4. In this paper we define an almost self-complementary 3-uniform hypergraph on n vertices and prove that it exists if and only if n is congruent to 3 modulo 4. The structure of corresponding complementing permutation is also analyzed. Further, we prove that there does not exist a regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent to 3 modulo 4, and it is proved that there exist a quasi regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent to 3 modulo 4.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 131-140
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decomposing complete 3-uniform hypergraph $K_n^{(3)}$ into 7-cycles
Autorzy:
Meihua, -
Guan, Meiling
Jirimutu, -
Powiązania:
https://bibliotekanauki.pl/articles/1397516.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
uniform hypergraph
7-cycle
cycle decomposition
Opis:
We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete k-uniform hypergraph $K_n^{(k)}$ into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For $ n \equiv 2,4, 5 (mod 6)$, we design an algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of $ K_n^{(3)}$ into 5-cycles has been presented for all admissible $ n \leq 17$, and for all $n = 4^m + 1$ when $m$ is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we show if $42 | (n — 1)(n — 2)$ and if there exist $\lambda = (n-1)(n-2)/42$ sequences $(k_{i0}, k_{i1},…..,k_{i6})$ on $D_{\text{all}}(n)$, then $K_n^{(3)}$ can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of $K_{37}^{(3)}$ and $K_{43}^{(3)}$ into 7-cycles.
Źródło:
Opuscula Mathematica; 2019, 39, 3; 383-393
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Tytuł:
Families of triples with high minimum degree are Hamiltonian
Autorzy:
Rödl, Vojtech
Ruciński, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/30148238.pdf
Data publikacji:
2014-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
3-uniform hypergraph
Hamilton cycle
minimum vertex degree
Opis:
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least $$(\frac{5−√5}{3} + γ)\binom{n−1}{2}$$ contains a tight Hamiltonian cycle.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 361-381
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A hierarchy of maximal intersecting triple systems
Autorzy:
Polcyn, J.
Ruciński, A.
Powiązania:
https://bibliotekanauki.pl/articles/254859.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
maximal intersecting family
3-uniform hypergraph
triple system
Opis:
We reach beyond the celebrated theorems of Erdös-Ko-Rado and Hilton-Milner, and a recent theorem of Han-Kohayakawa, and determine all maximal intersecting triples systems. It turns out that for each n ≥ 7 there are exactly 15 pairwise non-isomorphic such systems (and 13 for n = 6). We present our result in terms of a hierarchy of Turan numbers [formula], s ≥ 1, where [formula] is a pair of disjoint triples. Moreover, owing to our unified approach, we provide short proofs of the above mentioned results (for triple systems only). The triangle C3 is defined as C3 = {{x1,y3,x2}, {x1,y2,x3}, {x2, y1,x3}}. Along the way we show that the largest intersecting triple system H on n ≥ 6 vertices, which is not a star and is triangle-free, consists of max{10, n} triples. This facilitates our main proof's philosophy which is to assume that H contains a copy of the triangle and analyze how the remaining edges of H intersect that copy.
Źródło:
Opuscula Mathematica; 2017, 37, 4; 597-608
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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