Majority Edge Colouring of Hypergraph

Let G = (V, E) be a hypergraph. A 1/k-majority (k+1)-edge-colouring of a hypergraph is an edge-colouring with k+1 colours such that for every vertex v and each colour i, at most floor(d(v)/k) hyperedges incident to v receive colour i. Motivated by a recent work of Pękała and Przybyło on majority edge-colouring in graphs, we prove that every hypergraph G with minimum degree delta(G) >= 2 r k^2 admits a 1/k-majority (k+1)-edge-colouring, where r = max_{e in E} |e|, by extending their key lemma.