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Strong ramsey properties of simplices |
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| Authors: | |
| Institution: | (1) Shibuya-ku, Higashi 1-14-4, 150-0011 Tokyo, Japan;(2) Department of Mathematics and Computer Science, Emory University, 30322 Atlanta, GA, USA |
| Abstract: | In this paper we will show that every simplexX with circumradiusϱ satisfies the following geometric partition property, which proves a conjecture from FR90]. For every positive realδ there exists a positive realσ such that everygc-colouring of then-dimensional sphere of radiusϱ+δ withχ≤(1+σ) n results in a monochromatic copy ofX. |
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