Geodesic
Sum-List Colouring of Unions of a Hypercycle and a Path with at Most Two Vertices in Common
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 893-917

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Given a hypergraph ℋ and a function f : V (ℋ) → ℕ, we say that ℋ is f-choosable if there is a proper vertex colouring ϕ of ℋ such that ϕ (v) ∈ L(v) for all v ∈ V (ℋ), where L : V (ℋ) → 2^ℕ is any assignment of f(v) colours to a vertex v. The sum choice number ℋi_sc(ℋ) of ℋ is defined to be the minimum of Σ_v∈V(ℋ)f(v) over all functions f such that ℋ is f-choosable. For an arbitrary hypergraph ℋ the inequality χ_sc(ℋ) ≤ |V (ℋ)| + |ɛ (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.
Keywords: hypergraphs, sum-list colouring, induced hereditary classes, forbidden hypergraphs 
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Drgas-Burchardt, Ewa; Sidorowicz, Elżbieta. Sum-List Colouring of Unions of a Hypercycle and a Path with at Most Two Vertices in Common. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 893-917. http://geodesic.mathdoc.fr/item/DMGT_2020_40_3_a13/