Determine piercing by stars in the subquadratic range

Determine the asymptotics of g(n,Kp|K1,p−1), and more generally of g(n,Kp|K1,q) for p≤2q−2.

Background

Theorem 9.40 gives estimates for star piercing, including the quadratic regime, but leaves the stated subquadratic ranges unresolved.

References

Problem 10.25. Determine the asymptotics of g(n, Kpl(K1,p-1)), and more generally of g(n, Kpl(K1,q)) for p≤ 2q-2.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.25, Section 10.2