A graph with R red, G green, B blue edges contains at most ¼(RGB)^{2/3} properly colored K4s, with equality only for balanced blowups of a properly colored K4; the known rainbow-triangle bound √(2RGB) receives new flag-algebra, counting, and entropy proofs.
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Density of rainbow triangles and properly colored $K_4$'s
A graph with R red, G green, B blue edges contains at most ¼(RGB)^{2/3} properly colored K4s, with equality only for balanced blowups of a properly colored K4; the known rainbow-triangle bound √(2RGB) receives new flag-algebra, counting, and entropy proofs.