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COCOA
2010
Springer

The Union of Colorful Simplices Spanned by a Colored Point Set

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The Union of Colorful Simplices Spanned by a Colored Point Set
A simplex spanned by a colored point set in Euclidean d-space is colorful if all vertices have distinct colors. The union of all full-dimensional colorful simplices spanned by a colored point set is called the colorful union. We show that for every d N, the maximum combinatorial complexity of the colorful union of n colored points in Rd is between (n(d-1)2 ) and O(n(d-1)2 log n). For d = 2, the upper bound is known to be O(n), and for d = 3 we present an upper bound of O(n4 (n)), where (
André Schulz, Csaba D. Tóth
Added 10 Feb 2011
Updated 10 Feb 2011
Type Journal
Year 2010
Where COCOA
Authors André Schulz, Csaba D. Tóth
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