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Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find aminimum cardinality vertex cover of $G$ that induces a connected subgraph. Inthis paper we describe some approaches to solve the CVC problem exactly. First,we give compact mixed-integer extended formulations for CVC: these are thefirst formulations proposed for this problem, and can be easily adapted tovariations of the problem such as Tree Cover. Second, we describe a simplebranch and bound algorithm for the CVC problem. Finally, we implement ouralgorithm and compare its performance against our best formulation: contrary towhat usually happens for the classical Vertex Cover problem, our formulationoutperforms the branch and bound algorithm.

Exact approaches for the Connected Vertex Cover problem