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» On Planar Quasi-Parity Graphs
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ICALP
2003
Springer
15 years 3 months ago
Generating Labeled Planar Graphs Uniformly at Random
Abstract. We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that...
Manuel Bodirsky, Clemens Gröpl, Mihyun Kang
CORR
2002
Springer
115views Education» more  CORR 2002»
14 years 9 months ago
Simultaneous Embedding of a Planar Graph and Its Dual on the Grid
Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the ...
Cesim Erten, Stephen G. Kobourov
GD
2005
Springer
15 years 3 months ago
Non-planar Core Reduction of Graphs
We present a reduction method that reduces a graph to a smaller core graph which behaves invariant with respect to planarity measures like crossing number, skewness, and thickness....
Carsten Gutwenger, Markus Chimani
COMPGEOM
2010
ACM
15 years 2 months ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
JACM
2002
93views more  JACM 2002»
14 years 9 months ago
Map graphs
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planar...
Zhi-Zhong Chen, Michelangelo Grigni, Christos H. P...