Determine zero-sum Ramsey numbers for trees and forests over other finite groups

Determine the zero-sum Ramsey numbers for trees or forests over cyclic groups other than \mathbb{Z}_3, beginning with the prime-order groups \mathbb{Z}_p and, in particular, the case p=5.

Background

The paper completely determines R(F,\mathbb{Z}_3) for the forests considered, while emphasizing that corresponding problems for other groups remain substantially unresolved. The authors specifically suggest studying \mathbb{Z}_p for prime p, with \mathbb{Z}_5 as a possible first case.

Only isolated results are cited for these other groups, so a systematic determination for trees or forests would extend the paper's methods and classification beyond \mathbb{Z}_3.