The site's wording fails for every graph. Every graph is one of its own subgraphs, so a graph $G$ that is not Ramsey size linear always has a subgraph, $G$ itself, that is not Ramsey size linear; no graph qualifies, and the wording's answer is trivially no. The site's own example fails with the rest: $K_4$ is not Ramsey size linear, so not all of its subgraphs are. The change inserts the word "proper" before "subgraphs"; nothing else changes. The posers' own words fix the form. [EFRS93] defines the graphs asked for by edge deletion (Definition 2, p. 395: not Ramsey size linear, "but if any edge is deleted, then the resulting graph is Ramsey size linear"), says on the same page that three candidate graphs "would be minimal, since all of their proper subgraphs are Ramsey size linear", and asks for an infinite family of such graphs, or one other than $K_4$ (Question 6, p. 399). Erdős's restatement in [Er95] (item 9 of the combinatorics part, p. 12 of the reprint) presents $K(4)$ as an instance, "known not to be Ramsey size linear but all its subgraph [sic] are Ramsey size linear", which is true only of its proper subgraphs; so the omission of "proper" is already in [Er95], and the site follows that wording. The site's commentary names $K_4$ as the only known example, and the formal-conjectures statement quantifies over subgraphs $H<\top$, the proper ones; it counts with the site. Edge-deletion minimality and proper-subgraph minimality agree for graphs without isolated vertices (an elementary check: Ramsey size-linearity passes to subgraphs, since $R(H,F)\le R(G,F)$ for $H\subseteq G$, and a graph differing from $G$ only by isolated vertices is Ramsey size linear exactly when $G$ is, so a minimal graph has no isolated vertices and its proper subgraphs are the subgraphs of its one-edge-deleted graphs). No result about the site's wording is published. The problem's standing judges the corrected Statement.