Determine matching-based asymptotic constants

Determine the limits of f(n,K2p|pK2)/n and g(n,K2p|pK2)/n as n tends to infinity.

Background

The paper establishes linear upper and lower bounds for piercing by perfect matchings, differing by a constant factor. The limiting constants are not determined.

References

Problem 10.21. Determine lim f(n, K2p|(pK2)) and lim g(n, K2pk(pK2)) 200 n . 200 n

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.21, Section 10.2