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We study tensor models based on $O(N)^r$ symmetry groups constructed out ofrank-$r$ tensors with order-$q$ interaction vertices. We refer to those tensormodels for which $r<q-1$ as \textit{subchromatic}. We focus most of ourattention on sextic ($q=6$) models with maximally-single-trace interactions. Weshow that only three subchromatic sextic maximally-single-trace interactionvertices exist: these are the $r=3$ prism, the $r=3$ wheel (or $K_{3,3}$) andthe $r=4$ octahedron. For theories based on these interactions we demonstratethat the set of Feynman diagrams that contribute to the free energy in thelarge $N$ limit are melonic (or closely related to melonic diagrams, in thecase of the prism) and thus can be explicitly summed.

Melonic Dominance in Subchromatic Sextic Tensor Models