Characterize feasible asymptotic pairs

Characterize all feasible pairs (c,d) for the functions f and g.

Background

A feasible pair is defined by an asymptotic relation φ(n,G|F)∼c n^d with c>0 and 0≤d≤2. The paper gives examples but no full characterization.

References

Problem 10.11. Characterize the feasible pairs (c,d) for de {f, g}.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.11, Section 10.1