- 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