منابع مشابه
Colourful transversal theorems
We prove colourful versions of three classical transversal theorems: the Katchalski-Lewis Theorem “T(3) implies T-k”, the “T(3) implies T” Theorem for well distributed sets, and the Goodmann-Pollack Transversal Theorem
متن کاملColourful Simplicial Depth
Inspired by Bárány’s Colourful Carathéodory Theorem [4], we introduce a colourful generalization of Liu’s simplicial depth [13]. We prove a parity property and conjecture that the minimum colourful simplicial depth of any core point in any d-dimensional configuration is d2 +1 and that the maximum is dd+1 +1. We exhibit configurations attaining each of these depths, and apply our results to the ...
متن کاملMore Colourful Simplices
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in general position in R is contained in at least d(d + 1)/2e simplices with one vertex from each set. This improves the known lower bounds for all d ≥ 4.
متن کاملMinimizing Unsatisfaction in Colourful Neighbourhoods
Abstract. Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximising the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutio...
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Hans Holger Rath STEP Electronic Publishing Solutions GmbH, Rimpar, Germany [email protected] http://www.topicmaps.com/ Abstract: The new ISO standard ISO/IEC 13250 Topic Maps defines a model and architecture for the semantic structuring of link networks. Dubbed the “GPS of the information universe”, topic maps will become the solution for organizing and navigating large and continuously growi...
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ژورنال
عنوان ژورنال: Nature
سال: 1986
ISSN: 0028-0836,1476-4687
DOI: 10.1038/319715c0