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- W2090982263 abstract "Abstract For S ⊆ ℝ n a set C ⊆ S is an m -clique if the convex hull of no m -element subset of C is contained in S . We show that there is essentially just one way to construct a closed set S ⊆ ℝ 2 without an uncountable 3-clique that is not the union of countably many convex sets. In particular, all such sets have the same convexity number; that is, they require the same number of convex subsets to cover them. The main result follows from an analysis of the convex structure of closed sets in ℝ 2 without uncountable 3-cliques in terms of clopen, P 4 -free graphs on Polish spaces." @default.
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- W2090982263 date "2014-03-14" @default.
- W2090982263 modified "2023-09-30" @default.
- W2090982263 title "2-dimensional Convexity Numbers and P4-free Graphs" @default.
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- W2090982263 doi "https://doi.org/10.4153/cmb-2012-031-5" @default.
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