Determine anti-Ramsey numbers for odd cycles with matchings

Determine Ar(n,C2k+1∪K2), and more generally Ar(n,C2k+1∪mK2).

Background

These anti-Ramsey numbers arise in the analysis of g(n,p,q) when p=2q−2. The paper explains that related estimates are known but the exact general problem remains unresolved.

References

Problem 10.29. Determine Ar(n, C2k+1UK2), and more generally Ar(n, C2k+1U mK2).

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.29, Section 10.2