On a problem in combinatorial geometry
β
VojtΔch RΓΆdl
π
Article
π
1983
π
Elsevier Science
π
English
β 253 KB
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.