For every ε ≥ 1/2, the maximal anti-Ramsey function χ_S(n, C(n,2)−⌊n^{2−ε}⌋, P_4) exceeds n²/72 for sufficiently large n, establishing the quadratic lower bound in the complementary regime to Li–Ning–Xie's negative result.
Erd o s, On a theorem of Rademacher-Turán, Illinois J
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On the maximal anti-Ramsey problem of Burr, Erd\H{o}s, Graham, and S\'{o}s for $P_4$
For every ε ≥ 1/2, the maximal anti-Ramsey function χ_S(n, C(n,2)−⌊n^{2−ε}⌋, P_4) exceeds n²/72 for sufficiently large n, establishing the quadratic lower bound in the complementary regime to Li–Ning–Xie's negative result.