Clustered Planarity: Small Clusters in Cycles and Eulerian Graphs
نویسندگان
چکیده
منابع مشابه
Clustered Planarity: Small Clusters in Cycles and Eulerian Graphs
We present several polynomial-time algorithms for c-planarity testing for cluster hierarchy C containing clusters of size at most three. The main result is an O(|C| + n)-time algorithm for clusters of size at most three on a cycle. The result is then generalized to a special class of Eulerian graphs, namely graphs obtained from a 3-connected planar graph of fixed size k by multiplying and then ...
متن کاملClustered Planarity: Embedded Clustered Graphs with Two-Component Clusters
We present a polynomial-time algorithm for c-planarity testing of clustered graphs with fixed plane embedding and such that every cluster induces a subgraph with at most two connected components.
متن کاملClustered Graphs and C-planarity
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...
متن کاملC-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...
متن کاملC-Planarity of Extrovert Clustered Graphs
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2009
ISSN: 1526-1719
DOI: 10.7155/jgaa.00192