The operator structures that can contribute to three-nucleon forces are classified in the 1/Nc expansion. At leading order in 1/Nc a spin-flavor independent term is present, as are the spin-flavor structures associated with the Fujita-Miyazawa three-nucleon force. Modern phenomenological three-nucleon forces are thus consistent with this O(Nc) leading force, corrections to which are suppressed by a power series in 1/Nc^2. A complete basis of operators for the three-nucleon force, including all independent momentum structures, is given explicitly up to next-to-leading order in the 1/Nc expansion.
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