Clustering Cycles into Cycles of Clusters
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.
- 2.Biedl, T.C.: Drawing planar partitions III: Two constrained embedding problems. Tech. Report RRR 13-98, RUTCOR Rutgen University (1998)Google Scholar
- 4.Cortese, P.F., Di Battista, G., Patrignani, M., Pizzonia, M.: Clustering cycles into cycles of clusters. Technical Report RT-DIA-91-2004, Dipartimento di Informatica e Automazione, Universit‘a di Roma Tre, Rome, Italy (2004)Google Scholar
- 6.Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)Google Scholar
- 7.Even, S.: Graph Algorithms. Computer Science Press, Potomac (1979)Google Scholar
- 9.Feng, Q.W., Cohen, R.F., Eades, P.: Planarity for clustered graphs. In: Spirakis, P. (ed.) ESA 1995. LNCS, vol. 979, pp. 213–226. Springer, Heidelberg (1995)Google Scholar