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» Improved upper bounds on the crossing number
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CORR
2010
Springer
104views Education» more  CORR 2010»
13 years 7 months ago
Coloring translates and homothets of a convex body
We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of fini...
Adrian Dumitrescu, Minghui Jiang
COMGEO
2011
ACM
13 years 2 months ago
A computational approach to Conway's thrackle conjecture
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum ...
Radoslav Fulek, János Pach
LATA
2009
Springer
14 years 2 months ago
Automata on Gauss Words
In this paper we investigate the computational complexity of knot theoretic problems and show upper and lower bounds for planarity problem of signed and unsigned knot diagrams repr...
Alexei Lisitsa, Igor Potapov, Rafiq Saleh
CORR
2010
Springer
107views Education» more  CORR 2010»
13 years 4 months ago
Metric uniformization and spectral bounds for graphs
We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate "Riemannian" metric to uniformize th...
Jonathan A. Kelner, James R. Lee, Gregory N. Price...
TIT
2008
103views more  TIT 2008»
13 years 7 months ago
Improved Probabilistic Bounds on Stopping Redundancy
For a linear code , the stopping redundancy of is defined as the minimum number of check nodes in a Tanner graph T for such that the size of the smallest stopping set in T is equal...
Junsheng Han, Paul H. Siegel, Alexander Vardy