13 search results - page 1 / 3 » On the rectilinear crossing number of complete graphs |
SODA
2003
ACM
13 years 6 months ago
2003
ACM
We prove a lower bound of 0.3288 n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
JCT
2007
13 years 5 months ago
2007
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
ENDM
2008
13 years 5 months ago
2008
For n 27 we present exact values for the maximum number h(n) of halving lines and h(n) of halving pseudolines, determined by n points in the plane. For this range of values of n ...
GD
2006
Springer
13 years 8 months ago
2006
Springer
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
GD
2009
Springer
13 years 8 months ago
2009
Springer
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...