Bounds on the measurable chromatic number of Rn

L. A. Székely, N. C. Wormald

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We develop a method of estimating the (upper) density of a set in Rn or Sn for which the distance between any pair of points is not in a prescribed set. This is a generalisation of a planar principle of the first author. It improves the best known results for small values of n≥3. It also improves the known lower bounds on the measurable chromatic number of Rn for small n≥4.

Original languageEnglish
Pages (from-to)343-372
Number of pages30
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 1989
Externally publishedYes

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