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» A new upper bound on the cyclic chromatic number
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JCT
2007
103views more  JCT 2007»
13 years 7 months ago
Geometric drawings of Kn with few crossings
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...
Bernardo M. Ábrego, Silvia Fernández...
CORR
2010
Springer
179views Education» more  CORR 2010»
13 years 4 months ago
The DMM bound: multivariate (aggregate) separation bounds
In this paper we derive aggregate separation bounds, named after Davenport-MahlerMignotte (DMM), on the isolated roots of polynomial systems, specifically on the minimum distance ...
Ioannis Z. Emiris, Bernard Mourrain, Elias P. Tsig...
SODA
2000
ACM
114views Algorithms» more  SODA 2000»
13 years 8 months ago
Typical random 3-SAT formulae and the satisfiability threshold
: k-SAT is one of the best known among a wide class of random constraint satisfaction problems believed to exhibit a threshold phenomenon where the control parameter is the ratio, ...
Olivier Dubois, Yacine Boufkhad, Jacques Mandler
JGAA
2006
127views more  JGAA 2006»
13 years 7 months ago
A New Algorithm for Finding Minimal Cycle-Breaking Sets of Turns in a Graph
We consider the problem of constructing a minimal cycle-breaking set of turns for a given undirected graph. This problem is important for deadlock-free wormhole routing in compute...
Lev B. Levitin, Mark G. Karpovsky, Mehmet Mustafa,...
CORR
2010
Springer
168views Education» more  CORR 2010»
13 years 4 months ago
Bounds on the maximum multiplicity of some common geometric graphs
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in genera...
Adrian Dumitrescu, André Schulz, Adam Sheff...