Abstract
Thep-partitioning andp-coloring problems on a Bethe lattice of coordination numberz are analyzed. It is shown that these two NP-complete optimization problems turn out to be equivalent to finding the ground-state energy ofp-state Potts models with frustration. Numerical calculation of the cost function of both problems are carried out for several values ofz andp. In the case ofp=2 the results are identical to those obtained by Mézard and Parisi for the case of the bipartitioning problem. A numerical upper bound to the chromatic number is found for several values ofz.
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de Oliveira, M.J. Graph optimization problems on a Bethe lattice. J Stat Phys 54, 477–493 (1989). https://doi.org/10.1007/BF01023490
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DOI: https://doi.org/10.1007/BF01023490