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Wyświetlanie 1-10 z 23
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
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:
Sum-List Colouring of Unions of a Hypercycle and a Path with at Most Two Vertices in Common
Autorzy:
Drgas-Burchardt, Ewa
Sidorowicz, Elżbieta
Powiązania:
https://bibliotekanauki.pl/articles/31527293.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraphs
sum-list colouring
induced hereditary classes
forbidden hypergraphs
Opis:
Given a hypergraph \(\mathcal{H}\) and a function \(f : V (\mathcal{H}) → ℕ\), we say that \(\mathcal{H}\) is $f$-choosable if there is a proper vertex colouring $ϕ$ of \(\mathcal{H}\) such that $ϕ (v) ∈ L(v)$ for all \(v ∈ V (\mathcal{H})\), where \(L : V (\mathcal{H}) → 2^ℕ\) is any assignment of $f(v)$ colours to a vertex $v$. The sum choice number \(\mathcal{H}i_{sc}(\mathcal{H})\) of \(\mathcal{H}\) is defined to be the minimum of \(Σ_{v∈V(\mathcal{H})}f(v)\) over all functions $f$ such that \(\mathcal{H}\) is $f$-choosable. For an arbitrary hypergraph \(\mathcal{H}\) the inequality \(χ_{sc}(\mathcal{H}) ≤ |V (\mathcal{H})| + |ɛ (\mathcal{H})|\) holds, and hypergraphs that attain this upper bound are called $sc$-greedy. In this paper we characterize $sc$-greedy hypergraphs that are unions of a hypercycle and a hyperpath having at most two vertices in common. Consequently, we characterize the hypergraphs of this type that are forbidden for the class of $sc$-greedy hypergraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 893-917
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:
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:
Recursion Relations for Chromatic Coefficients for Graphs and Hypergraphs
Autorzy:
Durhuus, Bergfinnur
Lucia, Angelo
Powiązania:
https://bibliotekanauki.pl/articles/32361749.pdf
Data publikacji:
2022-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
chromatic polynomials
hypergraphs
broken cycles
Opis:
We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney’s broken cycle theorem for hypergraphs, as well as deriving an explicit formula for the linear coefficient of the chromatic polynomial of the r-complete hypergraph in terms of roots of the Taylor polynomials for the exponential function.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 101-121
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The size of minimum 3-trees: cases 0 and 1 mod 12
Autorzy:
Arocha, Jorge
Tey, Joaquín
Powiązania:
https://bibliotekanauki.pl/articles/743397.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tight hypergraphs
triple systems
Opis:
A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic triple and the hypergraph has the minimum possible number of triples. There is a conjecture that the number of triples in such 3-tree is ⎡(n(n-2))/3⎤ for any number of vertices n. Here we give a proof of this conjecture for any n ≡ 0,1 mod 12.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 177-187
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 of self-complementary hypergraphs
Autorzy:
Zwonek, M.
Powiązania:
https://bibliotekanauki.pl/articles/255199.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
self-complementary hypergraphs
complementing permutation
Opis:
In the paper we describe all self-complementary hypergraphs. It turns out that such hypergraphs exist if and only if the number of vertices of the hypergraph is of the form n = 2k. This answers a conjecture posed by A. Szymański (see[3]).
Źródło:
Opuscula Mathematica; 2005, 25, 2; 351-354
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
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