Results 1 to 10 of about 782 (118)
Clustered Planarity with Pipes [PDF]
Algorithmica, 2019 19 pages, 9 figures, extended version of the paper appeared at ISAAC ...
Patrizio Angelini, Giordano da Lozzo
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Clustered Planarity = Flat Clustered Planarity [PDF]
Lecture Notes in Computer Science, 2018 The complexity of deciding whether a clustered graph admits a clustered planar drawing is a long-standing open problem in the graph drawing research area. Several research efforts focus on a restricted version of this problem where the hierarchy of the clusters is "flat", i.e., no cluster different from the root contains other clusters.
Maurizio Patrignani
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C-Planarity of C-Connected Clustered Graphs [PDF]
Journal of Graph Algorithms and Applications, 2008 We present the first characterization of c-planarity for c-connected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the ...
Pier Francesco Cortese +4 more
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Relaxing the constraints of clustered planarity
Computational Geometry: Theory and Applications, 2015 In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions. A drawing of a clustered graph is c-planar if it has no edge-edge, edge-region, or region-region crossings.
Fabrizio Frati +2 more
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Clustered Planarity Testing Revisited [PDF]
Lecture Notes in Computer Science, 2014 The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward ...
Radoslav Fulek +2 more
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Clustered Planarity: Clusters with Few Outgoing Edges [PDF]
Lecture Notes in Computer Science, 2009 We present a linear algorithm for c-planarity testing of clustered graphs, in which every cluster has at most four outgoing edges.
Ondřej Suchy +2 more
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Clustered Planarity: Small Clusters in Cycles and Eulerian Graphs
Journal of Graph Algorithms and Applications, 2009 We present several polynomial-time algorithms for c-planarity testing for cluster hierarchy C containing clusters of size at most three. The main result is an O(|C|3 + n)-time algorithm for clusters of size at most three on a cycle.
Eva Jelínková +5 more
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Clustered Planarity: Embedded Clustered Graphs with Two-Component Clusters [PDF]
Lecture Notes in Computer Science, 2009 We present a polynomial-time algorithm for c-planarity testing of clustered graphs with fixed plane embedding and such that every cluster induces a subgraph with at most two connected components.
Bernard Lidický +2 more
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C-Planarity of Extrovert Clustered Graphs [PDF]
Lecture Notes in Computer Science, 2006 A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The c-planarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions and with each edge (drawn as a curve between vertex points ...
Michael Goodrich
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Shrinking the Search Space for Clustered Planarity [PDF]
Lecture Notes in Computer Science, 2013 A clustered graph is a graph augmented with a hierarchical inclusion structure over its vertices, and arises very naturally in multiple application areas. While it is long known that planarity--i.e., drawability without edge crossings--of graphs can be tested in polynomial (linear) time, the complexity for the clustered case is still unknown.
Markus Chimani, Karsten Klein 0001
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