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...
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1, 2, . . . , c. Motivated by conjectures of Propp, we are led to consider partitions of ...
The paper deals with a solution of a fuzzy interval system of linear equations, i.e. a system in which fuzzy intervals (numbers) appear instead of crisp numbers. We obtain general...
Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their ele...
We prove that the lines tangent to four possibly intersecting convex polyhedra in 3 with n edges in total form Θ(n2 ) connected components in the worst case. In the generic ca...