Sum-list colouring of unions of a hypercycle and a path with at most two vertices in common
Ewa Drgas‐Burchardt, Elżbieta Sidorowicz · Discussiones Mathematicae Graph Theory · 2020
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 of H such that (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 vV (H) f (v) over all functions f such that H is f -choosable. For an arbitrary hypergraph H the inequality sc (H) |V (H)| + |E(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.