On the unbalanced cut problem and the generalized Sherrington-Kirkpatrick model

We establish a strict asymptotic inequality between a class of graph partition problems on the sparse End\H{o]s-R'enyi and random regular graph ensembles with the same average degree. Along the way, we establish a variational representation for the ground state energy for generalized mixed $p$-spin glasses and derive strict comparison inequalities for such models as the alphabet changes.