Strong ramsey properties of simplices | Zendy

Péter Frankl | Zendy; Vojtěch Rödl | Zendy

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Strong ramsey properties of simplices

Author(s) -

Péter Frankl,

Vojtěch Rödl

Publication year - 2004

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02787550

Subject(s) - mathematics , conjecture , partition (number theory) , monochromatic color , combinatorics , radius , property (philosophy) , existential quantification , discrete mathematics , philosophy , botany , computer security , epistemology , computer science , biology

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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