Affirmative resolution of χ_S(n,⌊un⌋,P4)<Cu and negative resolution showing χ_S(n,binom(n,2)−⌊n^{2−ε}⌋,P4)=o(n²) for fixed ε>0.
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Two problems of Burr, Erd\H os, Graham, and S\'os on maximal anti-Ramsey functions for $P_4$
Affirmative resolution of χ_S(n,⌊un⌋,P4)<Cu and negative resolution showing χ_S(n,binom(n,2)−⌊n^{2−ε}⌋,P4)=o(n²) for fixed ε>0.