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The induced q-color size-Ramsey number r₈₍₃ (H;q) of a graph H is the minimal number of edges a host graph G can have so that every q-edge-coloring of G contains a monochromatic copy of H which is an induced subgraph of G. A natural question, which in the non-induced case has a very long history, asks which families of graphs H have induced Ramsey numbers that are linear in |H|. We prove that for every k, w, q, if H is an n-vertex graph with maximum degree k and treewidth at most w, then r₈₍₃ (H;q) = O₊, ₖ, ₐ (n). This extends several old and recent results in Ramsey theory. Our proof is quite simple and relies upon a novel reduction argument.
Hunter et al. (Sat,) studied this question.