A EUCLIDEAN RAMSEY THEOREM

Authors
BONA M
Citation
M. Bona, A EUCLIDEAN RAMSEY THEOREM, Discrete mathematics, 122(1-3), 1993, pp. 349-352
Citations number
NO
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Discrete mathematics → ACNP
ISSN journal
0012365X
Volume
122
Issue
1-3
Year of publication
1993
Pages
349 - 352
Database
ISI
SICI code
0012-365X(1993)122:1-3<349:AERT>2.0.ZU;2-S
Abstract
In this note we shall prove a geometric Ramsey theorem. Let T be a tri angle with angles 30, 60 and 90 degrees, and with hypotenus of unit le ngth. Then the theorem says that if one three-colors the 3-space, then there is always a copy of T with monochromatic vertices. We shall als o show that there is a 12-coloration of the space in which there is no copy of T with monochromatic vertices.