SIAM Journal on Computing
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Planarization of Clustered Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A Linear Time Algorithm to Recognize Clustered Graphs and Its Parallelization
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Journal of Computer and System Sciences
A new approach for visualizing UML class diagrams
Proceedings of the 2003 ACM symposium on Software visualization
How to draw the minimum cuts of a planar graph
Computational Geometry: Theory and Applications
Automatic layout of UML class diagrams in orthogonal style
Information Visualization - Special issue: Software visualization
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Drawing c-planar biconnected clustered graphs
Discrete Applied Mathematics
Clustered Planarity: Clusters with Few Outgoing Edges
Graph Drawing
Computing Maximum C-Planar Subgraphs
Graph Drawing
Straight-Line Rectangular Drawings of Clustered Graphs
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
The SPQR-tree data structure in graph drawing
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Efficient C-planarity testing for embedded flat clustered graphs with small faces
GD'07 Proceedings of the 15th international conference on Graph drawing
Clustered planarity: small clusters in Eulerian graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
On embedding a cycle in a plane graph
GD'05 Proceedings of the 13th international conference on Graph Drawing
C-planarity of extrovert clustered graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Clustering cycles into cycles of clusters
GD'04 Proceedings of the 12th international conference on Graph Drawing
Splitting clusters to get c-planarity
GD'09 Proceedings of the 17th international conference on Graph Drawing
Shrinking the search space for clustered planarity
GD'12 Proceedings of the 20th international conference on Graph Drawing
Completely connected clustered graphs
Journal of Discrete Algorithms
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A clustered graph C = (G, T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G = (V, E). Each vertex 碌 in T corresponds to a subset of the vertices of the graph called "cluster". c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automaticgraph drawing. The complexity status of c-planarity testing is unknown. It has been shown in [FCE95, Dah98] that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected.In this paper, we provide a polynomial time algorithm for c-planarity testing of "almost" c-connected clustered graphs, i.e., graphs for which all nodes corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each nonconnected cluster its super-cluster and all its siblings in T are connected. The algorithm is based on the concepts for the subgraph induced planar connectivity augmentation problem presented in [GJL+02]. We regard it as a first step towards general c-planarity testing.