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In this paper we study non-commutative Yang-Mills theory (NCYM) through itsgravity dual. First it is shown that the gravity dual of an NCYM with self-dual$\theta$-parameters has a Lagrangian in the form of five-dimensional dilatonicgravity. Then we use the de-Boer-Verlinde-Verlinde formalism for holographicrenormalization group flows to calculate the coefficient functions in the Weylanomaly of the NCYM at low energies under the assumption of potentialdominance, and show that the $C$-theorem holds true in the present case.Comment: 22pp. Totally different method and new results that supercede earlier  hep-th/991219

The c-functions of noncommutative Yang-Mills theory from holography