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A ramsey-type bound for rectangles

✍ Scribed by T�th, G�za

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 199 KB
Volume: 23
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199609)23:1<53::aid-jgt6>3.0.co;2-j

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✦ Synopsis

It is proved that for any rectangle T and for any 2-coloring of the points of the 5dimensional Euclidean space, one can always find a rectangle T' congruent to T , all of whose vertices are of the same color. We also show that for any k-coloring of the k2 + o(k2)-dimensional space, there is a monochromatic rectangle congruent to any given rectangle.

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