Exponents for Hamiltonian paths on random bicubic maps and KPZ

We evaluate the configuration exponents of various ensembles Hamiltonian paths drawn on random planar bicubic maps. These are estimated from extrapolations exact enumeration results for finite sizes and compared with their theoretical predictions based Knizhnik, Polyakov Zamolodchikov (KPZ) relations, as applied to regular counterpart honeycomb lattice. show that a naive use these relations does not reproduce measured but simple modification in application may possibly correct observed discrepancy. similar is required via KPZ formulas some exactly known problem unweighted fully packed loops