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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
Tytuł:
The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
Autorzy:
Kamble, Lata N.
Deshpande, Charusheela M.
Bam, Bhagyashree Y.
Powiązania:
https://bibliotekanauki.pl/articles/31340929.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
self-complementary hypergraph
uniform hypergraph
regular hypergraph
quasi regular hypergraph
bi-regular hypergraph
Opis:
A k-uniform hypergraph H = (V; E) is called self-complementary if there is a permutation σ : V → V, called a complementing permutation, 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 ; V(k) − E). In this paper we define a bi-regular hypergraph and prove that there exists a bi-regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 or 2 modulo 4. We also prove that there exists a quasi regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 modulo 4.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 419-426
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Tytuł:
Covering the Edges of a Random Hypergraph by Cliques
Autorzy:
Rödl, Vojtěch
Ruciński, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/32222535.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
r-uniform random hypergraph
clique covering
Opis:
We determine the order of magnitude of the minimum clique cover of the edges of a binomial, r-uniform, random hypergraph G(r)(n, p), p fixed. In doing so, we combine the ideas from the proofs of the graph case (r = 2) in Frieze and Reed [Covering the edges of a random graph by cliques, Combinatorica 15 (1995) 489–497] and Guo, Patten, Warnke [Prague dimension of random graphs, manuscript submitted for publication].
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1333-1349
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the α-Spectral Radius of Uniform Hypergraphs
Autorzy:
Guo, Haiyan
Zhou, Bo
Powiązania:
https://bibliotekanauki.pl/articles/31551887.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
adjacency tensor
uniform hypergraph
extremal hypergraph
α-spectral radius
α-Perron vector
Opis:
For \(0 ≤ \alpha < 1\) and a uniform hypergraph $G$, the \(\alpha\)-spectral radius of $G$ is the largest $H$-eigenvalue of \(\alpha\mathcal{D}(G)+(1−\alpha)\mathcal{A}(G)\), where \(\mathcal{D}(G)\) and \(\mathcal{A}(G)\) are the diagonal tensor of degrees and the adjacency tensor of $G$, respectively. We give upper bounds for the \(\alpha\)-spectral radius of a uniform hypergraph, propose some transformations that increase the \(\alpha\)-spectral radius, and determine the unique hypergraphs with maximum \(\alpha\)-spectral radius in some classes of uniform hypergraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 559-575
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Wyświetlanie 1-15 z 17

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