Recent studies of holographic properties of massless higher-order gravities, whose linear spectrum contains only the (massless) graviton, yielded some universal relations in d = 4 dimensions between the holographic a and c charges and the overall coefficient factor C T of the energy-momentum tensor two-point function, namely, c = 1 d ? 1 ? ? a ? ? = C T , where ? is the anti–de Sitter radius. The second equality was shown to be valid in all dimensions. In this paper, we establish the first equality in d = 6 by examining these quantities from D = 7 higher-order gravities. Consequently, the overall coefficient of the two-point function of the energy-momentum tensor is proportional to this c charge, generalizing the well-known d = 4 result. We identify the relevant c charge as the coefficient of a specific combination of the three type-B anomalies. Modulo total derivatives, this combination involves the Riemann tensor at most linearly.
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