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A Problem in Combinatorial Geometry

✍ Scribed by Hall, R. R.

Book ID
120096174
Publisher
Oxford University Press
Year
1976
Tongue
English
Weight
96 KB
Volume
s2-12
Category
Article
ISSN
0024-6107

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A problem in combinatorial geometry
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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.