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Clustered Planarity with Pipes [PDF]
Algorithmica, 2019 19 pages, 9 figures, extended version of the paper appeared at ISAAC ...
Patrizio Angelini +2 more
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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.
Patrignani Maurizio
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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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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
doaj +2 more sources
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: 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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NodeTrix Planarity Testing with Small Clusters [PDF]
Algorithmica, 2019 We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant $k$. We consider both the case when the sides of the matrices to which the edges are incident are fixed and the case when they can be chosen arbitrarily. We show that NodeTrix planarity testing with fixed sides can be
Alessandra Tappini +2 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, Goodrich Michael T
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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.
Karsten Klein, Chimani Markus
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