  In this work, a graph partitioning problem in a fixed number of connected
components is considered. Given an undirected graph with costs on the edges,
the problem consists on partitioning the set of nodes into a fixed number of
subsets with minimum size, where each subset induces a connected subgraph with
minimal edge cost. Mixed Integer Programming formulations together with a
variety of valid inequalities are demonstrated and implemented in a Branch &
Cut framework. A column generation approach is also proposed for this problem
with additional cuts. Finally, the methods are tested for several simulated
instances and computational results are discussed.
