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ALGORITHMICA
2010
156views more  ALGORITHMICA 2010»
14 years 11 months ago
On Covering Problems of Rado
T. Rado conjectured in 1928 that if S is a finite set of axis-parallel squares in the plane, then there exists an independent subset I S of pairwise disjoint squares, such that I ...
Sergey Bereg, Adrian Dumitrescu, Minghui Jiang
CCCG
2007
15 years 8 days ago
A Lower Bound on the Area of a 3-Coloured Disc Packing
Given a set of unit-discs in the plane with union area A, what fraction of A can be covered by selecting a pairwise disjoint subset of the discs? Rado conjectured
Peter Brass, Ferran Hurtado, Benjamin J. Lafrenier...
EJC
2010
14 years 11 months ago
On graphs isomorphic to their neighbour and non-neighbour sets
The paper contains a construction of a universal countable graph, different from the Rado graph, such that for any of its vertices both the neighbourhood and the non-neighbourhood ...
Przemyslaw Gordinowicz
JCT
2010
113views more  JCT 2010»
14 years 9 months ago
Equations resolving a conjecture of Rado on partition regularity
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...
Boris Alexeev, Jacob Tsimerman
CORR
2010
Springer
67views Education» more  CORR 2010»
14 years 8 months ago
Covering Cubes and the Closest Vector Problem
Friedrich Eisenbrand, Nicolai Hähnle, Martin ...