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.