Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Advances in C-Planarity Testing of Clustered Graphs
GD '02 Revised Papers from the 10th 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
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
C-planarity of extrovert clustered graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Shrinking the search space for clustered planarity
GD'12 Proceedings of the 20th international conference on Graph Drawing
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In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the Split-C-Planarity problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that Split-C-Planarity is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected series-parallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters.