Abstract
In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are “highly non connected”. We start by studying 3-cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the c-planarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3-cluster cycles in terms of formal grammars. Finally, we generalize the results on 3-cluster cycles considering clustered graphs that at each level of the inclusion tree have a cycle structure. Even in this case we show efficient c-planarity testing and drawing algorithms.
Work partially supported by European Commission – Fet Open project COSIN – COevolution and Self-organisation In dynamical Networks – IST-2001-33555, by European Commission – Fet Open project DELIS – Dynamically Evolving Large Scale Information Systems – Contract no 001907, by “Progetto ALINWEB: Algoritmica per Internet e per il Web”, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale, and by “The Multichannel Adaptive Information Systems (MAIS) Project”, MIUR–FIRB.
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Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M. (2005). Clustering Cycles into Cycles of Clusters. In: Pach, J. (eds) Graph Drawing. GD 2004. Lecture Notes in Computer Science, vol 3383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31843-9_12
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DOI: https://doi.org/10.1007/978-3-540-31843-9_12
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