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- W4310283104 abstract "A classical vertex Ramsey result due to Nev{s}etv{r}il and Rodl states that given a finite family of graphs $mathcal{F}$, a graph $A$ and a positive integer $r$, if every graph $Binmathcal{F}$ has a $2$-vertex-connected subgraph which is not a subgraph of $A$, then there exists an $mathcal{F}$-free graph which is vertex $r$-Ramsey with respect to $A$. We prove that this sufficient condition for the existence of an $mathcal{F}$-free graph which is vertex $r$-Ramsey with respect to $A$ is also necessary for large enough number of colours $r$. We further show a generalisation of the result to a family of graphs and the typical existence of such a subgraph in a dense binomial random graph." @default.
- W4310283104 created "2022-11-30" @default.
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- W4310283104 date "2022-11-25" @default.
- W4310283104 modified "2023-09-27" @default.
- W4310283104 title "On vertex Ramsey graphs with forbidden subgraphs" @default.
- W4310283104 doi "https://doi.org/10.48550/arxiv.2211.13966" @default.
- W4310283104 hasPublicationYear "2022" @default.
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