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Claim. Problem 79 asks whether there are infinitely many graphs which are not Ramsey size linear although all of their proper subgraphs are. Wigderson answers yes. Theorem 1 of Infinitely many minimally non-Ramsey size-linear graphs says that infinitely many graphs fail to be Ramsey size-linear while each of their proper subgraphs has the property; the statement, its lemmas and a proof pointer are on the result page. The half-page proof argues by contradiction: were there only finitely many minimal examples, a graph of average degree at least $4$ and girth larger than all their cycle lengths would contain none of them, yet by the Erdős--Faudree--Rousseau--Schelp edge bound it is not Ramsey size-linear, so an inclusion-minimal non-Ramsey-size-linear subgraph of it is a further minimal example. The argument exhibits no graph beyond $K_4$; the paper's Open problem 5 asks for one, and that question is not the problem's.

Scope. Full. The theorem is the problem page's corrected Statement, which asks about graphs all of whose proper subgraphs are Ramsey size linear; the site's wording, which omits "proper", admits no graph at all, as the page's Notes record. The paper's edge-deletion minimality and the proper-subgraph minimality agree for graphs without isolated vertices, as the problem page checks.

Depends on. Nothing in this wiki; the result rests on the cited paper alone.

Acceptance. Reviewed: the site's curator, T. F. Bloom, labels the problem PROVED and credits the paper with the proof in the problem's commentary, noting that the proof is not explicit and that no example beyond $K_4$ is known; the thread and the proof-claim tab were empty on 2026-09-18. Refereed: the paper appeared in European J. Combin. 128 (2025), 104175 (the acknowledgments thank the anonymous referees). The text cited is arXiv v2 of 5 May 2025. Proof coverage: the statement, Lemmas 2--4 and Open problem 5; the proof is not compiled in this corpus.

Postings. arXiv:2409.05931, v1 of 9 September 2024 (the first posting, which dates this page) and v2 of 5 May 2025, the version cited; the journal article; the site's problem page, whose thread and proof-claim tab were empty on 2026-09-18. The formal-conjectures file for the problem is a statement with no proof and is not a formalization of this result.