Clustered Planarity: Embedded Clustered Graphs with Two-Component Clusters
نویسندگان
چکیده
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.
منابع مشابه
Efficient c-planarity testing algebraically
We generalize the strong Hanani-Tutte theorem to clustered graphs with two disjoint clusters, and show that an extension of our result to flat clustered graphs with three disjoint clusters is not possible. We also give a new and short proof for a result by Di Battista and Frati about efficient c-planarity testing of an embedded flat clustered graph with small faces based on the matroid intersec...
متن کاملSubexponential-Time and FPT Algorithms for Embedded Flat Clustered Planarity
The C-Planarity problem asks for a drawing of a clustered graph, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edgeedge crossings, no region-region crossings, and no unnecessary edge-region crossings. We study C-Planarity for embedded flat clustered graphs, graphs with a fixed combinatorial embedding whose...
متن کاملClustered Planarity Testing Revisited
The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three o...
متن کاملC-Planarity of C-Connected Clustered Graphs Part I – Characterization
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...
متن کاملAdvances on Testing C-Planarity of Embedded Flat Clustered Graphs
We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008