Abstract
A clustered graph C = (G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G = (V,E). Each vertex μ in T corresponds to a subset of the vertices of the graph called “cluster”. c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automaticgraph drawing. The complexity status of c-planarity testing is unknown. It has been shown in [FCE95,Dah98] that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected.
In this paper, we provide a polynomial time algorithm for c-planarity testing of “almost” c-connected clustered graphs, i.e., graphs for which all nodes corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each nonconnected cluster its super-cluster and all its siblings in T are connected. The algorithm is based on the concepts for the subgraph induced planar connectivity augmentation problem presented in [GJL+02]. We regard it as a first step towards general c-planarity testing.
Partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).
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Gutwenger, C., Jünger, M., Leipert, S., Mutzel, P., Percan, M., Weiskircher, R. (2002). Advances in C-Planarity Testing of Clustered Graphs. In: Goodrich, M.T., Kobourov, S.G. (eds) Graph Drawing. GD 2002. Lecture Notes in Computer Science, vol 2528. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36151-0_21
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DOI: https://doi.org/10.1007/3-540-36151-0_21
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