We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε > 0 there is a δ > 0 such that for n sufficiently large...
Suppose one wishes to compare two closely related systems via stochastic simulation. Common random numbers (CRN) involves using the same streams of uniform random variates as inpu...
Recurrence relations are derived for the numbers of labeled 3-regular graphs with given connectivity, order, number of double edges, and number of loops. This work builds on metho...
Gab-Byung Chae, Edgar M. Palmer, Robert W. Robinso...
G. Leibon and D. Letscher showed that for general and sufficiently dense point set its Delaunay triangulation and Voronoi diagram in Riemannian manifold exist. They also proposed ...
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...