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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 549.05029

**Autor: ** Eggleton, R.B.; Erdös, Paul; Skilton, D.K.

**Title: ** Colouring the real line. (In English)

**Source: ** J. Comb. Theory, Ser. B 39, 86-100 (1985); Errata ibid. 41, 139 (1986).

**Review: ** We discuss the problem of colouring the real line so that the distance between like coloured numbers does not lie in some specified set D, called the distance set. In particular, we determine the minimum number of colours needed for various distance sets.
The errata correct construction details in the proof of Theorem 4, and two other
subsequent details.

**Reviewer: ** P.Erdös

**Classif.: ** * 05C15 Chromatic theory of graphs and maps

05A17 Partitions of integres (combinatorics)

**Keywords: ** chromatic number; infinite graphs; finite subgraphs; real numbers; positive
integers; prime numbers; coloured numbers; distance set

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