Exact Approaches for the Connected Vertex Cover Problem

Given a graph G, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of G that induces a connected subgraph. This paper describes some approaches to solve the CVC problem exactly. First, we give compact mixed-integer extended formulations for CVC: these are the first formulations proposed for this problem, have a small number of extra variables and can be easily adapted to variations of the problem such as Tree Cover. Second, we describe a simple branch and bound algorithm for the CVC problem. Finally, we implement our algorithm and compare its performance against our best extended formulation: contrary to what usually happens for the classical Vertex Cover problem, our formulation outperforms the branch and bound algorithm.