Determine the growth of f(n,K4|3(-P3))

Prove or disprove that f(n,K4|3(-P3)) is linear in n.

Background

The paper gives the bounds 2n−2≤f(n,K4|3(-P3))=O(n{3/2}) and notes that the exact order is unresolved. The case n=4 is known exactly, but the asymptotic behavior is open.

References

Problem 10.20. Prove or disprove that f(n, K4|3(-P3)) is linear in n.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.20, Section 10.2