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103
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DCG
2011
14 years 5 months ago
More 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 Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...
Antoine Deza, Tamon Stephen, Feng Xie
62
Voted
VRML
1999
ACM
15 years 2 months ago
Less is More: The Power of Simplicity
Jean-Francis Balaguer
CORR
2007
Springer
116views Education» more  CORR 2007»
14 years 10 months ago
Frugal Colouring of Graphs
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
Omid Amini, Louis Esperet, Jan van den Heuvel
COLOGNETWENTE
2009
14 years 11 months ago
Acyclic and Frugal Colourings of Graphs
Given a graph G = (V, E), a proper vertex colouring of V is t-frugal if no colour appears more than t times in any neighbourhood and is acyclic if each of the bipartite graphs con...
Ross J. Kang, Tobias Müller
83
Voted
JCO
2008
153views more  JCO 2008»
14 years 10 months ago
A quadratic lower bound for colourful simplicial depth
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.
Tamon Stephen, Hugh Thomas