Abstract
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.
Work partially supported by MUR under Project MAINSTREAM Algorithms for Massive Information Structures and Data Streams.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Cornelsen, S., Wagner, D.: Completely connected clustered graphs. Journal of Discrete Algorithms 4(2), 313–323 (2006)
Cortese, P.F., Di Battista, G.: Clustered planarity. In: ACM SoCG 2005, pp. 32–34 (2005)
Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M.: Clustering cycles into cycles of clusters. Journal of Graph Algorithms and Applications 9(3), 391–413 (2005)
Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M.: On embedding a cycle in a plane graph. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 49–60. Springer, Heidelberg (2006)
Dahlhaus, E.: A linear time algorithm to recognize clustered graphs and its parallelization. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 239–248. Springer, Heidelberg (1998)
Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. Tech. Report RT-DIA-119-2007, Dip. Inf. e Aut., Univ. Roma Tre (2007)
Feng, Q., Cohen, R.F., Eades, P.: Planarity for clustered graphs. In: Spirakis, P.G. (ed.) ESA 1995. LNCS, vol. 979, pp. 213–226. Springer, Heidelberg (1995)
Goodrich, M.T., Lueker, G.S., Sun, J.Z.: C-planarity of extrovert clustered graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 211–222. Springer, Heidelberg (2006)
Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R.: Advances in c-planarity testing of clustered graphs. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 220–235. Springer, Heidelberg (2002)
Kirkpatrick, D.G.: Establishing order in planar subdivisions. Discrete & Computational Geometry 3, 267–280 (1988)
Nishizeki, T., Chiba, N.: Planar Graphs: Theory and Algorithms. North-Holland (1988)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Di Battista, G., Frati, F. (2008). Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces . In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-77537-9_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77536-2
Online ISBN: 978-3-540-77537-9
eBook Packages: Computer ScienceComputer Science (R0)