C-Planarity of C-Connected Clustered Graphs
نویسندگان
چکیده
منابع مشابه
C-Planarity of C-Connected Clustered Graphs
We present the first characterization of c-planarity for c-connected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchies of the triconnected and biconnected components of the underlying graph. Based on such a characterization, we provide a linear-time c-planarity testing and embedding algorithm for c-connected clustered grap...
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We present a linear time algorithm for testing clustered planarity of c-connected clustered graphs and for computing a clustered planar embedding for such graphs. Our algorithm uses a decomposition of the input graph based on SPQR-trees and is the first linear time algorithm for clustered planarity testing. We define a normal form of clustered embeddings and show that a clustered graph is clust...
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We present a characterization of the c-planarity of c-connected clustered graphs. The characterization is based on the interplay between the hierarchy of the clusters and the hierarchy of the triconnected and biconnected components of the graph underlying the clustered graph. In a companion paper [2] we exploit such a characterization to give a linear time c-planarity testing and embedding algo...
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In this paper, we introduce a new graph model known as clustered graphs, i.e. graphs with recursive clustering structures. This graph model has many applications in informational and mathematical sciences. In particular, we study C-planarity of clustered graphs. Given a clustered graph, the C-planarity testing problem is to determine whether the clustered graph can be drawn without edge crossin...
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A clustered graph has its vertices grouped into clusters in a hierarchical way via subset inclusion, thereby imposing a tree structure on the clustering relationship. The c-planarity problem is to determine if such a graph can be drawn in a planar way, with clusters drawn as nested regions and with each edge (drawn as a curve between vertex points) crossing the boundary of each region at most o...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2008
ISSN: 1526-1719
DOI: 10.7155/jgaa.00165