منابع مشابه
Clustered 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 کاملPlanarity Testing Revisited
Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by Allender and Mahajan [AM00] with the aid of Reingold’s result [Rei08]. Unfortunately, the algorithm is quite daunting and generalizing it to say, the bounded ...
متن کاملPlanarity Testing for C-Connected Clustered Graphs
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...
متن کاملClustered Level Planarity
Planarity is an important concept in graph drawing. It is generally accepted that planar drawings are well understandable. Recently, several variations of planarity have been studied for advanced graph concepts such as k-level graphs [6,10–16] and clustered graphs [5,7]. In k-level graphs, the vertices are partitioned into k levels and the vertices of one level are drawn on a horizontal line. I...
متن کاملAdvances in C-Planarity Testing of Clustered Graphs
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 c 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 automatic graph drawing. The complexity status of ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/5002