Prove or refute the universal n+8 upper-bound conjecture

Prove or refute the conjecture that R(G,\mathbb{Z}_3) is at most n+8 for every graph G on n vertices with 3 dividing e(G), and characterize the equality case by determining whether equality occurs if and only if G is a triangle.

Background

The paper conjectures a universal upper bound for zero-sum Ramsey numbers over \mathbb{Z}_3. The conjecture applies to every graph G with n vertices whose number of edges is divisible by 3, extending beyond the forests treated in the paper.

The proposed extremal case is the triangle: the conjecture asserts both the bound R(G,\mathbb{Z}_3) leq n+8 and the precise equality characterization. Establishing it would give a general quantitative bound for the entire class of admissible graphs.