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SODA
2010
ACM
248views Algorithms» more  SODA 2010»
14 years 1 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
13 years 11 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 4 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 2 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....