For d-degenerate graphs satisfying m ≥ 2pd(d+1)^2, p|m and 2d<p, the zero-sum Ramsey number R(G, Z_p) is at most n + (3+3d)p.
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A linear upper bound on zero-sum Ramsey numbers of $d$-degenerate graphs in $\mathbb{Z}_p$
For d-degenerate graphs satisfying m ≥ 2pd(d+1)^2, p|m and 2d<p, the zero-sum Ramsey number R(G, Z_p) is at most n + (3+3d)p.