Bounds on the measurable chromatic number of Rn

L. A. Székely; N. C. Wormald

doi:10.1016/0012-365X(89)90099-X

Bounds on the measurable chromatic number of Rⁿ

L. A. Székely, N. C. Wormald

Research output: Contribution to journal › Article › Research › peer-review

17 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	343-372
Number of pages	30
Journal	Discrete Mathematics
Volume	75
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(89)90099-X
Publication status	Published - 1989
Externally published	Yes

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10.1016/0012-365X(89)90099-X

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AB - 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.

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DO - 10.1016/0012-365X(89)90099-X

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VL - 75

SP - 343

EP - 372

JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Bounds on the measurable chromatic number of Rn

Abstract

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Bounds on the measurable chromatic number of Rⁿ