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» Lower bounds on the obstacle number of graphs
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COMGEO
2011
ACM
13 years 2 months ago
On crossing numbers of geometric proximity graphs
Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed prox...
Bernardo M. Ábrego, Ruy Fabila Monroy, Silv...
JCT
2007
90views more  JCT 2007»
13 years 7 months ago
On the maximum number of edges in quasi-planar graphs
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...
Eyal Ackerman, Gábor Tardos
SODA
2010
ACM
248views Algorithms» more  SODA 2010»
14 years 5 months ago
Approximating the Crossing Number of Graphs Embeddable in Any Orientable Surface
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...
Petr Hlineny, Markus Chimani
ARSCOM
2004
124views more  ARSCOM 2004»
13 years 7 months ago
The Domatic Number of Regular Graphs
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
Peter Dankelmann, Neil J. Calkin
ISPAN
2002
IEEE
14 years 22 days ago
Automatic Processor Lower Bound Formulas for Array Computations
In the directed acyclic graph (dag) model of algorithms, consider the following problem for precedence-constrained multiprocessor schedules for array computations: Given a sequenc...
Peter R. Cappello, Ömer Egecioglu