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COMGEO
2004
ACM
13 years 10 months ago
Convexity minimizes pseudo-triangulations
The number of minimum pseudo-triangulations is minimized for point sets in convex position. 2004 Elsevier B.V. All rights reserved.
Oswin Aichholzer, Franz Aurenhammer, Hannes Krasse...
GD
2006
Springer
14 years 1 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle
FOCS
2006
IEEE
14 years 4 months ago
On a Geometric Generalization of the Upper Bound Theorem
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Uli Wagner
IWPEC
2004
Springer
14 years 3 months ago
The Minimum Weight Triangulation Problem with Few Inner Points
We propose to look at the computational complexity of 2-dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, poi...
Michael Hoffmann, Yoshio Okamoto
CORR
2010
Springer
104views Education» more  CORR 2010»
13 years 10 months ago
Coloring translates and homothets of a convex body
We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of fini...
Adrian Dumitrescu, Minghui Jiang