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Wyświetlanie 1-15 z 68
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 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:
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:
Asymptotic Sharpness of Bounds on Hypertrees
Autorzy:
Lin, Yi
Kang, Liying
Shan, Erfang
Powiązania:
https://bibliotekanauki.pl/articles/31341637.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypertree
semicycle in hypergraph
chain in hypergraph
Opis:
The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a $k$-uniform hypertree on $n$ vertices has at most \( \binom{n}{k−1} \) edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of $k$-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of $k$-uniform $k$-hypertrees.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 789-795
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Niche Hypergraphs of Products of Digraphs
Autorzy:
Sonntag, Martin
Teichert, Hanns-Martin
Powiązania:
https://bibliotekanauki.pl/articles/32083765.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
niche hypergraph
product of digraphs
competition hypergraph
Opis:
If $ D = (V, A) $ is a digraph, its niche hypergraph \( N \mathcal{H} (D) = (V, \mathcal{E} ) \) has the edge set \( \mathcal{E} = \{ e \subseteq V \ | \ |e| \le 2 \land \exists υ \in V : e = N_D^− (υ) \lor e=N_D^+ (υ) \} \). Niche hypergraphs generalize the well-known niche graphs and are closely related to competition hypergraphs as well as common enemy hypergraphs. For several products \( D_1 \circ D_2 \) of digraphs \( D_1 \) and \( D_2 \), we investigate the relations between the niche hypergraphs of the factors \( D_1 \), \( D_2 \) and the niche hypergraph of their product \( D_1 \circ D_2 \).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 279-295
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
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:
Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges
Autorzy:
Fan, Yi-Zheng
Tan, Ying-Ying
Peng, Xi-Xi
Liu, An-Hong
Powiązania:
https://bibliotekanauki.pl/articles/31340758.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tensor
spectral radius
unicyclic hypergraph
bicyclic hypergraph
girth
Opis:
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 845-856
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
Packing of nonuniform hypergraphs - product and sum of sizes conditions
Autorzy:
Naroski, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/744492.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nonuniform hypergraph
packing
Opis:
Hypergraphs $H₁,...,H_N$ of order n are mutually packable if one can find their edge disjoint copies in the complete hypergraph of order n. We prove that two hypergraphs are mutually packable if the product of their sizes satisfies some upper bound. Moreover we show that an arbitrary set of the hypergraphs is mutually packable if the sum of their sizes is sufficiently small.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 3; 651-656
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
ℤ2 × ℤ2 -Cordial Cycle-Free Hypergraphs
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/32361757.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
V 4 -cordial graph
hypergraph
labeling of hypergraph
hyper-tree
Opis:
Hovey introduced A-cordial labelings as a generalization of cordial and harmonious labelings [7]. If A is an Abelian group, then a labeling f : V (G) → A of the vertices of some graph G induces an edge labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. The problem of A-cordial labelings of graphs can be naturally extended for hypergraphs. It was shown that not every 2-uniform hypertree (i.e., tree) admits a ℤ2 × ℤ2-cordial labeling [8]. The situation changes if we consider p-uniform hypertrees for a bigger p. We prove that a p-uniform hypertree is ℤ2 × ℤ2-cordial for any p > 2, and so is every path hypergraph in which all edges have size at least 3. The property is not valid universally in the class of hypergraphs of maximum degree 1, for which we provide a necessary and sufficient condition.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1021-1040
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
Tytuł:
High Girth Hypergraphs with Unavoidable Monochromatic or Rainbow Edges
Autorzy:
Axenovich, Maria
Karrer, Annette
Powiązania:
https://bibliotekanauki.pl/articles/32361723.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraph
chromatic number
mixed hypergraph
bihyper-graphs
monochromatic
rainbow
girth
selective
Opis:
A classical result of Erdős and Hajnal claims that for any integers k, r, g ≥ 2 there is an r-uniform hypergraph of girth at least g with chromatic number at least k. This implies that there are sparse hypergraphs such that in any coloring of their vertices with at most k − 1 colors there is a monochromatic hyperedge. When there is no restriction on the number of the colors used, one can easily avoid monochromatic hyperedges. Then, however, so-called rainbow or multicolored hyperedges might appear. Nešetřil and Rödl [19] called hypergraphs such that in any vertex-coloring there is either a monochromatic or a rainbow hyperedge, selective. They showed an existence of selective r-uniform hypergraphs of girth g for any integers r, g ≥ 2 using probabilistic and explicit constructions. In this paper, we provide a slightly di erent construction of such hypergraphs and summarize the probabilistic approaches. The main building block of the construction, a part-rainbow-forced hypergraph, is of independent interest. This is an r-uniform r-partite hypergraph with a given girth such that in any vertex-coloring that is rainbow on each part, there is a rainbow hyperedge. We give a simple construction of such a hypergraph that does not use iterative amalgamation.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 471-484
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a list colouring of hypergraphs
Autorzy:
Drgas-Burchardt, E.
Powiązania:
https://bibliotekanauki.pl/articles/2050379.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
hypergraph
list colouring
Opis:
In the note we present two results. The first of them gives a sufficient condition for a colouring of a hypergraph from an assigned list. It generalises the analogous fact for graphs. The second result states that for every $k \geq 3$ and every $l \geq 2$, a distance between the list chromatic number and the chromatic number can be arbitrarily large in the class of k-uniform hypergraphs with the chromatic number bounded below by l. A similar result for k-uniform, 2-colorable hypergraphs is known but the proof techniques are different.
Źródło:
Opuscula Mathematica; 2004, 24, 2; 171-175
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 68

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