Temat: hypergraphs - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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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