منابع مشابه
Colourful transversal theorems
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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 ...
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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.
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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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ژورنال
عنوان ژورنال: Nature Chemistry
سال: 2014
ISSN: 1755-4330,1755-4349
DOI: 10.1038/nchem.2078