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Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

Tytuł:: $ \mathcal{P} $-Apex Graphs
Autorzy:: Borowiecki, Mieczysław
Drgas-Burchardt, Ewa
Sidorowicz, Elżbieta
Powiązania:: https://bibliotekanauki.pl/articles/31342421.pdf
Data publikacji:: 2018-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: induced hereditary classes of graphs
forbidden subgraphs
hypergraphs
transversal number
Opis:: Let $ \mathcal{P} $ be an arbitrary class of graphs that is closed under taking induced subgraphs and let $ \mathcal{C}( \mathcal{P} ) $ be the family of forbidden subgraphs for $ \mathcal{P} $. We investigate the class $ \mathcal{P} (k) $ consisting of all the graphs $ G $ for which the removal of no more than $ k $ vertices results in graphs that belong to $ \mathcal{P} $. This approach provides an analogy to apex graphs and apex-outerplanar graphs studied previously. We give a sharp upper bound on the number of vertices of graphs in $ \mathcal{C}( \mathcal{P}(1)) $ and we give a construction of graphs in $ \mathcal{C}( \mathcal{P}(k)) $ of relatively large order for $ k \ge 2 $. This construction implies a lower bound on the maximum order of graphs in $ \mathcal{C}( \mathcal{P}(k)) $. Especially, we investigate $ \mathcal{C}( \mathcal{W}_r(1)) $, where $ \mathcal{W}_r $ denotes the class of $ \mathcal{P}_r $-free graphs. We determine some forbidden subgraphs for the class $ \mathcal{W}_r(1) $ with the minimum and maximum number of vertices. Moreover, we give sufficient conditions for graphs belonging to $ \mathcal{C} ( \mathcal{P} (k)) $, where $ \mathcal{P} $ is an additive class, and a characterisation of all forests in $ \mathcal{C} ( \mathcal{P} (k)) $. Particularly we deal with $ \mathcal{C} ( \mathcal{P} (1)) $, where $ \mathcal{P} $ is a class closed under substitution and obtain a characterisation of all graphs in the corresponding $ \mathcal{C} ( \mathcal{P} (1)) $. In order to obtain desired results we exploit some hypergraph tools and this technique gives a new result in the hypergraph theory.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 2; 323-349
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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