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Wyświetlanie 1-15 z 44
Tytuł:
Sum labellings of cycle hypergraphs
Autorzy:
Teichert, Hanns-Martin
Powiązania:
https://bibliotekanauki.pl/articles/743801.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraphs
sum number
vertex labelling
Opis:
A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph $_{d̲,[d̅]} (S) = (V,)$ where V = S and $ = {e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_{v∈ e} v ∈ S}$. For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices $y₁,..., y_σ ∉ V$ such that $ ∪ {y₁,...,y_σ}$ is a sum hypergraph.
Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this class of cycle hypergraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 2; 255-265
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classes of hypergraphs with sum number one
Autorzy:
Teichert, Hanns-Martin
Powiązania:
https://bibliotekanauki.pl/articles/743701.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraphs
sum number
vertex labelling
Opis:
A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ with 1 < d̲ < d̅ such that ℋ is isomorphic to the hypergraph $ℋ_{d̲,d̅}(S) = (V,)$ where V = S and $ = {e ⊆ S: d̲ < |e| < d̅ ∧ ∑_{v∈ e} v∈ S}$. For an arbitrary hypergraph ℋ the sum number(ℋ ) is defined to be the minimum number of isolatedvertices $w₁,..., w_σ∉ V$ such that $ℋ ∪ {w₁,..., w_σ}$ is a sum hypergraph.
For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs ₙ and ₙ that under a certain condition for the edgecardinalities (ₙ)= (ₙ)=1
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 93-103
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Chromatic polynomials of hypergraphs
Autorzy:
Borowiecki, Mieczysław
Łazuka, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/743817.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
chromatic polynomial
chromatically unique hypergraphs
chromatic characterization
Opis:
In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hypergraphs are chromatically unique. Moreover we give some equalities for the chromatic polynomials of hypergraphs generalizing known results for graphs and hypergraphs of Read and Dohmen.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 2; 293-301
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The sum number of d-partite complete hypergraphs
Autorzy:
Teichert, Hanns-Martin
Powiązania:
https://bibliotekanauki.pl/articles/744247.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
sum number
sum hypergraphs
d-partite complete hypergraph
Opis:
A d-uniform hypergraph is a sum hypergraph iff there is a finite S ⊆ IN⁺ such that is isomorphic to the hypergraph $ ⁺_d(S) = (V,)$, where V = S and $ = {{v₁,...,v_d}: (i ≠ j ⇒ v_i ≠ v_j)∧ ∑^d_{i=1} v_i ∈ S}$. For an arbitrary d-uniform hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices $w₁,...,w_σ ∉ V$ such that $ ∪{ w₁,..., w_σ}$ is a sum hypergraph.
In this paper, we prove
$σ(^{d}_{n₁,...,n_d}) = 1 + ∑^d_{i=1} (n_i -1 ) + min{0,⌈1/2(∑_{i=1}^{d-1} (n_i -1) - n_d)⌉}$,
where $^{d}_{n₁,...,n_d}$ denotes the d-partite complete hypergraph; this generalizes the corresponding result of Hartsfield and Smyth [8] for complete bipartite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 1; 79-91
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximal hypergraphs with respect to the bounded cost hereditary property
Autorzy:
Drgas-Burchardt, Ewa
Fiedorowicz, Anna
Powiązania:
https://bibliotekanauki.pl/articles/744307.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cost colouring
hereditary property
maximal hypergraphs
Opis:
The hereditary property of hypergraphs generated by the cost colouring notion is considered in the paper. First, we characterize all maximal graphs with respect to this property. Second, we give the generating function for the sequence describing the number of such graphs with the numbered order. Finally, we construct a maximal hypergraph for each admissible number of vertices showing some density property. All results can be applied to the problem of information storage.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 67-77
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Directed hypergraphs: a tool for researching digraphs and hypergraphs
Autorzy:
Galeana-Sánchez, Hortensia
Manrique, Martín
Powiązania:
https://bibliotekanauki.pl/articles/743191.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraph
strongly independent set
transversal set
kernel
Opis:
In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level of any edge they belong to. Some little adjustments are needed to avoid directed walks within a single edge of the underlying hypergraph, and to deal with isolated vertices.
The concepts of independent set, absorbent set, and transversal set are inherited directly from digraphs.
As a consequence of our results on this topic, we have found both a class of kernel-perfect digraphs with odd cycles and a class of hypergraphs which have a strongly independent transversal set.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 313-335
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
About uniquely colorable mixed hypertrees
Autorzy:
Niculitsa, Angela
Voloshin, Vitaly
Powiązania:
https://bibliotekanauki.pl/articles/743697.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
colorings of graphs and hypergraphs
mixed hypergraphs
unique colorability
trees
hypertrees
elimination ordering
Opis:
A mixed hypergraph is a triple = (X,,) where X is the vertex set and each of , is a family of subsets of X, the -edges and -edges, respectively. A k-coloring of is a mapping c: X → [k] such that each -edge has two vertices with the same color and each -edge has two vertices with distinct colors. = (X,,) is called a mixed hypertree if there exists a tree T = (X,) such that every -edge and every -edge induces a subtree of T. A mixed hypergraph is called uniquely colorable if it has precisely one coloring apart from permutations of colors. We give the characterization of uniquely colorable mixed hypertrees.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 81-91
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:
Subgraph densities in hypergraphs
Autorzy:
Peng, Yuejian
Powiązania:
https://bibliotekanauki.pl/articles/743780.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Erdös jumping constant conjecture
Lagrangian
optimal vector
Opis:
Let r ≥ 2 be an integer. A real number α ∈ [0,1) is a jump for r if for any ε > 0 and any integer m ≥ r, any r-uniform graph with n > n₀(ε,m) vertices and density at least α+ε contains a subgraph with m vertices and density at least α+c, where c = c(α) > 0 does not depend on ε and m. A result of Erdös, Stone and Simonovits implies that every α ∈ [0,1) is a jump for r = 2. Erdös asked whether the same is true for r ≥ 3. Frankl and Rödl gave a negative answer by showing an infinite sequence of non-jumps for every r ≥ 3. However, there are still a lot of open questions on determining whether or not a number is a jump for r ≥ 3. In this paper, we first find an infinite sequence of non-jumps for r = 4, then extend one of them to every r ≥ 4. Our approach is based on the techniques developed by Frankl and Rödl.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 281-297
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Short paths in 3-uniform quasi-random hypergraphs
Autorzy:
Polcyn, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/744576.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraph
path
quasi-randomness
Opis:
Frankl and Rödl [3] proved a strong regularity lemma for 3-uniform hypergraphs, based on the concept of δ-regularity with respect to an underlying 3-partite graph. In applications of that lemma it is often important to be able to "glue" together separate pieces of the desired subhypergraph. With this goal in mind, in this paper it is proved that every pair of typical edges of the underlying graph can be connected by a hyperpath of length at most seven. The typicality of edges is defined in terms of graph and hypergraph neighborhoods, and it is shown that all but a small fraction of edges are indeed typical.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 469-484
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Packing of Uniform Hypergraphs
Autorzy:
Konarski, Jerzy
Woźniak, Mariusz
Żak, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/32222532.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing
hypergraphs
Opis:
We say that two n-vertex hypergraphs H1 and H2 pack if they can be found as edge-disjoint subhypergraphs of the complete hypergraph Kn. Whilst the problem of packing of graphs (i.e., 2-uniform hypergraphs) has been studied extensively since seventies, much less is known about packing of k-uniform hypergraphs for k ≥ 3. Naroski [Packing of nonuniform hypergraphs - product and sum of sizes conditions, Discuss. Math. Graph Theory 29 (2009) 651–656] defined the parameter mk(n) to be the smallest number m such that there exist two n-vertex k-uniform hypergraphs with total number of edges equal to m which do not pack, and conjectured that mk(n) = Θ (nk−1). In this note we show that this conjecture is far from being truth. Namely, we prove that the growth rate of mk(n) is of order nk/2 exactly for even k’s and asymptotically for odd k’s.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1383-1388
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
Maximum Hypergraphs without Regular Subgraphs
Autorzy:
Kim, Jaehoon
Kostochka, Alexandr V.
Powiązania:
https://bibliotekanauki.pl/articles/30147226.pdf
Data publikacji:
2014-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraphs
set system
subgraph
regular graph
Opis:
We show that an n-vertex hypergraph with no r-regular subgraphs has at most $2^{n−1}+r−2$ edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, $2^{n−1}$ distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 151-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Constrained Colouring and σ-Hypergraphs
Autorzy:
Caro, Yair
Lauri, Josef
Zarb, Christina
Powiązania:
https://bibliotekanauki.pl/articles/31339148.pdf
Data publikacji:
2015-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
σ-hypergraphs
constrained colourings
hypergraph colourings
Opis:
A constrained colouring or, more specifically, an $(\alpha, \beta)$-colouring of a hypergraph $H$, is an assignment of colours to its vertices such that no edge of $H$ contains less than $\alpha$ or more than $\beta$ vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of hypergraphs. In fact, for $r$-uniform hypergraphs, classical colourings correspond to $(2, r)$-colourings while an important instance of Voloshin colourings of $r$-uniform hypergraphs gives $(2, r−1)$-colourings. One intriguing aspect of all these colourings, not present in classical colourings, is that $H$ can have gaps in its $(\alpha, \beta)$-spectrum, that is, for $k_1 < k_2 < k_3$, $H$ would be $(\alpha, \beta)$-colourable using $k_1$ and using $k_3$ colours, but not using $k_2$ colours. In an earlier paper, the first two authors introduced, for $\sigma$ being a partition of $r$, a very versatile type of $r$-uniform hypergraph which they called $\sigma$-hypergraphs. They showed that, by simple manipulation of the parameters of a $\sigma$-hypergraph $H$, one can obtain families of hypergraphs which have $(2, r − 1)$-colourings exhibiting various interesting chromatic properties. They also showed that, if the smallest part of $\sigma$ is at least 2, then $H$ will never have a gap in its $(2, r − 1)$-spectrum but, quite surprisingly, they found examples where gaps re-appear when $\alpha = \beta = 2$. In this paper we extend many of the results of the first two authors to more general $(\alpha, \beta)$-colourings, and we study the phenomenon of the disappearance and re-appearance of gaps and show that it is not just the behaviour of a particular example but we place it within the context of a more general study of constrained colourings of $\sigma$-hypergraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 1; 171-189
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on packing of two copies of a hypergraph
Autorzy:
Pilśniak, Monika
Woźniak, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/743647.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing
hypergraphs
Opis:
A 2-packing of a hypergraph is a permutation σ on V() such that if an edge e belongs to (), then σ (e) does not belong to ().
We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V() and has at most 1/2n edges is 2-packable.
A 1-uniform hypergraph of order n with more than 1/2n edges shows that this result cannot be improved by increasing the size of .
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 45-49
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 44

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