Claims

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2007_06_27_alon_sudakov: Alon and Sudakov (J. Graph Theory 56, 2007): for a small absolute c > 0 no n-vertex graph has a clique and an independent set of size log n in every induced subgraph on c(log n)^3/log log n vertices; refereed; partial.

2020_04_09_alon_bucic_sudakov: Alon, Bucić and Sudakov (Proc. Amer. Math. Soc. 149, 2021) build n-vertex graphs in which every 2^{2^{(log log n)^{1/2+o(1)}}} vertices contain a clique and an independent set of size log n; refereed; partial.

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