# Covering graphs with convex sets and partitioning graphs into convex sets

## TL;DR

This paper explores the computational complexity of covering and partitioning graphs into convex sets under various convexity notions, advancing understanding of these problems in graph theory.

## Contribution

It provides new complexity results for covering and partitioning graphs into convex sets across multiple convexity types.

## Key findings

- Complexity results for covering graphs with convex sets.
- Complexity results for partitioning graphs into convex sets.
- Analysis across digital, monophonic, P3, and P3* convexities.

## Abstract

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.