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, 2012 A topological graph is \emph{$k$-quasi-planar} if it does not contain $k$ pairwise crossing edges. A topological graph is \emph{simple} if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy \cite{pach} showed that every $n$-vertex simple $k$-quasi-planar graph contains at ...
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Journal of Combinatorial Theory, Series B, 1998 Given four distinct vertices in a 4-connected planar graph \(G\), we characterize when the graph \(G\) contains a \(K_4\)-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has no \(K_4\)-subdivision with specified degree three vertices, if ...
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Algorithmica, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bruckdorfer, Till +2 more
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Bruckdorfer, Till +2 more
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SIAM Journal on Computing, 1992
The graph partitioning problem is the problem of dividing a given graph of \(n\) nodes into two sets of prescribed size while cutting a minimum number of edges. The authors show that the partitioning problem of a planar graph can be solved in polynomial time if the cutsize of the optimal partition is \(O(\log n)\) or if an embedding of the graph is ...
Bui, Thang Nguyen, Peck, Andrew
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The graph partitioning problem is the problem of dividing a given graph of \(n\) nodes into two sets of prescribed size while cutting a minimum number of edges. The authors show that the partitioning problem of a planar graph can be solved in polynomial time if the cutsize of the optimal partition is \(O(\log n)\) or if an embedding of the graph is ...
Bui, Thang Nguyen, Peck, Andrew
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Drawing Planar Graphs Symmetrically, III: Oneconnected Planar Graphs
Algorithmica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong, Seok-Hee, Eades, Peter
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Drawing Planar Graphs Symmetrically, II: Biconnected Planar Graphs
Algorithmica, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong, Seok-Hee, Eades, Peter
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1998
Abstract A graph G is planar if it can be drawn in the plane or on the surface of a sphere so that no two edges meet, except at a vertex at which both are incident. Such a drawing partitions the set of points of the plane or sphere not lying on G into faces; for example, the following drawing has 6 faces.
Ronald C Read, Robin J Wilson
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Abstract A graph G is planar if it can be drawn in the plane or on the surface of a sphere so that no two edges meet, except at a vertex at which both are incident. Such a drawing partitions the set of points of the plane or sphere not lying on G into faces; for example, the following drawing has 6 faces.
Ronald C Read, Robin J Wilson
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