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We note that it is possible to construct a bond vertex model that displaysq-state Potts criticality on an ensemble of phi3 random graphs of arbitrarytopology, which we denote as ``thin'' random graphs in contrast to the fatgraphs of the planar diagram expansion.  Since the four vertex model in question also serves to describe the criticalbehaviour of the Ising model in field, the formulation reveals an isomorphismbetween the Potts and Ising models on thin random graphs. On planar graphs asimilar correspondence is present only for q=1, the value associated withpercolation.Comment: 6 pages, 5 figure

A Potts/Ising correspondence on thin graphs