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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
FOCS
2009
IEEE
14 years 2 months ago
Planarity Allowing Few Error Vertices in Linear Time
— We show that for every fixed k, there is a linear time algorithm that decides whether or not a given graph has a vertex set X of order at most k such that G − X is planar (w...
Ken-ichi Kawarabayashi
ENDM
2007
106views more  ENDM 2007»
13 years 7 months ago
Removing Even Crossings on Surfaces
In this paper we investigate how certain results related to the HananiTutte theorem can be extended from the plane to surfaces. We give a simple topological proof that the weak Ha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
SMI
2010
IEEE
120views Image Analysis» more  SMI 2010»
13 years 6 months ago
Single-Cycle Plain-Woven Objects
—It has recently been shown that if we twist an arbitrary subset of edges of a mesh on an orientable surface, the resulting extended graph rotation system (EGRS) can be used to i...
Qing Xing, Ergun Akleman, Jianer Chen, Jonathan L....