| MSC: | 05C07 | Degree sequences |
| 05C15 | Coloring of graphs and hypergraphs |
Abstract:
In this brief note, we give a positive answer to a question that has recently been asked by L.~Addario--Berry et al. in this journal, namely: Given a graph $G=(V,E)$ and for every vertex $v\in V$ a list \hbox{$D_v\subseteq\{0,1,\ldots, d(v)\}$} satisfying $|D_v|\geqq\fraq{d(v)}2+1$, does there necessarily exist a spanning subgraph $H$ of $G$ such that $d_H(v)\in D_v$ holds for every $v\inV$?