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» On generalized Ramsey numbers
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SODA
2003
ACM
103views Algorithms» more  SODA 2003»
13 years 10 months ago
On the rectilinear crossing number of complete graphs
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...
Uli Wagner
ARSCOM
2008
118views more  ARSCOM 2008»
13 years 9 months ago
Proper Partitions of a Polygon and k-Catalan Numbers
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 ...
Bruce E. Sagan
FSS
2008
88views more  FSS 2008»
13 years 9 months ago
Solution of a system of linear equations with fuzzy numbers
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...
Rostislav Horcík
DAM
2007
84views more  DAM 2007»
13 years 9 months ago
Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets
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...
Vera Kurková, Marcello Sanguineti
COMPGEOM
2004
ACM
14 years 2 months ago
The number of lines tangent to arbitrary convex polyhedra in 3D
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...
Hervé Brönnimann, Olivier Devillers, V...