Erdős Problem 809: an independent proof of the seven-cycle threshold
For every fixed integer k >= 3, the minimum number of colors in an edge-coloring of an n-vertex simple graph with at least floor(n^2/4)+1 edges, in which every copy of C_(2k+1) is rainbow, is (1/8 + o(1))n^2. The minimum is attained. The development combines Asad Shahab's seven-cycle proof, using an exact rational five-vertex certificate, with a formalization of the Bucić-Chen-Ma argument for longer odd cycles.
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