Claims

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1993_12_01_erdos_faudree_rousseau_schelp: The 1993 paper that posed the question proves Ramsey size linearity for connected graphs with at most p+1 edges, the graphs K_1+T_(p-1) and the graphs with Turán number O(n^(3/2)), each inside the corrected hypothesis.

2022_02_21_bradac_gishboliner_sudakov: Every subdivision of K_4 on at least six vertices is Ramsey size linear (SIAM J. Discrete Math. 2024, Theorem 4); each such graph meets the corrected hypothesis, so the corrected question has answer yes for them.

2026_09_28_barria: A September 2026 preprint claims that every graph with no K4 minor is Ramsey size linear with R(G,H) at most 624 v(G) e(H), covering every 2-tree; a partial result on the corrected question, unreviewed.

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