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Combinatorial Geometry Problems in Pattern Recognition

✍ Scribed by Braß


Publisher
Springer
Year
2002
Tongue
English
Weight
286 KB
Volume
28
Category
Article
ISSN
0179-5376

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On a problem in combinatorial geometry
✍ Vojtěch Rödl 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 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.