منابع مشابه
Completely Connected Clustered Graphs
Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is c-planar if and only if the underlying graph is p...
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 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 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 کاملPerfectness of clustered graphs
Given a clustered graph (G,V), that is, a graph G = (V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0-1 matrix M(G,V). Nevertheless, we observe that, given (G,V), it i...
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 Discrete Algorithms
سال: 2006
ISSN: 1570-8667
DOI: 10.1016/j.jda.2005.06.002