We present some complexity results concerning the problems of covering a graph with p convex sets and of partitioning a graph into p convex sets. The following convexities are considered: digital convexity, monophonic convexity, $P_3$-convexity, and $P_3^{⁎}$-convexity.

中文翻译：

---

用凸集覆盖图并将图划分成凸集

我们提出了一些复杂的结果，涉及用p个凸集覆盖图以及将图划分为p个凸集的问题。考虑以下凸度：数字凸度，单音凸度，$P_3$-凸性，和 $P_3^{⁎}$-凸性。