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Statement

Notation as on the Theorem 1 and Conjecture 1 pages.

Conjecture 2 (Part C, remark 2, p. 299, quoted). "Let $F$, $G$ be graphs, $F\not\xrightarrow[2]{}G$, $F\not\xrightarrow[2]{}F$. Then there exists an infinite family of vertex critical Ramsey graphs for $F$ which contain $G$."

The paper motivates the hypothesis $F\not\xrightarrow[2]{}G$ (p. 299): if $F\xrightarrow[2]{}G$, at most one Ramsey critical graph for $F$ contains $G$, namely $G$ itself when it is one, so the unrestricted question is false. By the equivalence 2)$\Leftrightarrow$3) of Conjecture 1, which the paper calls obvious, $F\not\xrightarrow[2]{}F$ means that $F$ has at least two edges. For partitions of vertices instead of edges the paper states that the analogue is true, with the proof to appear in a forthcoming paper of V. Müller, J. Nešetřil and V. Rödl (p. 299).

Source. J. Nešetřil and V. Rödl, The structure of critical Ramsey graphs, Acta Math. Acad. Sci. Hungar. 32 (1978), no. 3--4, 295--300, doi:10.1007/BF01902367; remarks 2) and 3) and Conjecture 2 on p. 299. Edition as on the source card.

Read depth. Claims checked: read clause by clause on the page image. Nothing here is independently reviewed.

Bears on

No problem page consumes this conjecture.