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» Lower bounds on the obstacle number of graphs
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COMGEO
2011
ACM
14 years 5 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»
14 years 9 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»
15 years 7 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»
14 years 9 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
15 years 2 months 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