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» On the Crossing Number of Almost Planar Graphs
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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
GD
2006
Springer
13 years 11 months ago
Planarity Testing and Optimal Edge Insertion with Embedding Constraints
The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-o...
Carsten Gutwenger, Karsten Klein, Petra Mutzel
ISBRA
2009
Springer
14 years 2 months ago
Untangling Tanglegrams: Comparing Trees by Their Drawings
A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in biology – to compare evolutiona...
Balaji Venkatachalam, Jim Apple, Katherine St. Joh...
ISAAC
2005
Springer
131views Algorithms» more  ISAAC 2005»
14 years 26 days ago
Orthogonal Drawings of Series-Parallel Graphs with Minimum Bends
In an orthogonal drawing of a planar graph G, each vertex is drawn as a point, each edge is drawn as a sequence of alternate horizontal and vertical line segments, and any two edge...
Xiao Zhou, Takao Nishizeki
CORR
2010
Springer
107views Education» more  CORR 2010»
13 years 4 months ago
Metric uniformization and spectral bounds for graphs
We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate "Riemannian" metric to uniformize th...
Jonathan A. Kelner, James R. Lee, Gregory N. Price...