  The minimum k-partition problem is a challenging combinatorial problem with a
diverse set of applications ranging from telecommunications to sports
scheduling. It generalizes the max-cut problem and has been extensively studied
since the late sixties. Strong integer formulations proposed in the literature
suffer from a prohibitive number of valid inequalities and integer variables.
In this work, we introduce two compact integer linear and semidefinite
reformulations that exploit the sparsity of the underlying graph and develop
fundamental results leveraging the power of chordal decomposition. Numerical
experiments show that the new formulations improve upon state-of-the-art.
