A connection between MAX $κ$-CUT and the inhomogeneous Potts spin glass in the large degree limit

We study the asymptotic behavior of the Max $κ$-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.

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