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On a problem in combinatorial geometry

✍ Scribed by Vojtěch Rödl

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
253 KB
Volume
45
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Let us fix a number a, O< a < 2. We join two p0int.s on the unit sphere Sm in the real m-space iff their distance is a. Denote the obtained graph by g,,,. We prove that the chromatic number x(9@,,,) tends to infinity when m --+ a. This gives a positive answer to a question of P. Erdiis.

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