499 search results - page 16 / 100 » On the Decay of Crossing Numbers |
JCT
2007
13 years 8 months ago
2007
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...
JCT
2007
13 years 8 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...
GD
2009
Springer
13 years 11 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...
SIAMNUM
2010
13 years 2 months ago
2010
A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like ...
COMBINATORICS
2006
13 years 8 months ago
2006
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....