Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces
Di Battista, Giuseppe and Frati, Fabrizio (2008) Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces. In: Graph Drawing 15th International Symposium, GD 2007, September 24-26, 2007, Sydney, Australia , pp. 291-302 (Official URL: http://dx.doi.org/10.1007/978-3-540-77537-9_29).
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Let C be a clustered graph and suppose that the planar embedding of its underlying graph is fixed. Is testing the c-planarity of $C$ easier than in the variable embedding setting? In this paper we give a first contribution towards answering the above question. Namely, we characterize c-planar embedded flat clustered graphs with at most five vertices per face and give an efficient testing algorithm for such graphs. The results are based on a more general methodology that shades new light on the c-planarity testing problem.
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