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. In this paper we describe 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, 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 formulation: contrary to what usually happens for the classical Vertex Cover problem, our formulation outperforms the branch and bound algorithm.

翻译：给定图$G$，连通顶点覆盖问题（CVC）要求找到一个最小基数的顶点覆盖，使得该顶点覆盖诱导的子图是连通的。本文描述了几种精确求解CVC问题的方法。首先，我们给出了CVC的紧凑混合整数扩展公式：这是针对该问题提出的首批公式，并且可以轻松适应问题的变体，例如树覆盖。其次，我们描述了一种简单的分支定界算法来解决CVC问题。最后，我们实现了该算法，并将其性能与最佳公式进行了比较：与经典顶点覆盖问题的通常情况相反，我们的公式优于分支定界算法。