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- W3200230894 abstract "Abstract We provide a simple characterization of simplicial complexes on few vertices that embed into the d -sphere. Namely, a simplicial complex on $$d+3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> vertices embeds into the d -sphere if and only if its non-faces do not form an intersecting family. As immediate consequences, we recover the classical van Kampen–Flores theorem and provide a topological extension of the Erdős–Ko–Rado theorem. By analogy with Fáry’s theorem for planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent." @default.
- W3200230894 created "2021-09-27" @default.
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- W3200230894 date "2023-03-28" @default.
- W3200230894 modified "2023-10-15" @default.
- W3200230894 title "Embedding Dimensions of Simplicial Complexes on Few Vertices" @default.
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- W3200230894 doi "https://doi.org/10.1007/s00026-023-00644-4" @default.
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