Completely connected clustered graphs

Cornelsen, Sabine; Wagner, Dorothea

doi:10.1016/j.jda.2005.06.002

Cited by 36 publications

(28 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• completely connected clustered graphs, that are c-connected clustered graphs such that the complement of the subgraph induced by each cluster is connected; an elegant characterization for this class is shown in [2].…”

Section: Introductionmentioning

confidence: 99%

Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces

Battista¹,

Frati²

2009

JGAA

View full text Add to dashboard Cite

Let C be a clustered graph and suppose that the planar embedding of its underlying graph is fixed. Is testing the c-planarity of C easier than in the variable embedding setting? In this paper we give a first contribution towards answering the above question. Namely, we characterize c-planar embedded flat clustered graphs with at most five vertices per face and give an efficient testing algorithm for such graphs. The results are based on a more general methodology that sheds new light on the c-planarity testing problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces

Battista¹,

Frati²

2009

JGAA

View full text Add to dashboard Cite

show abstract

“…Another interesting contribution is the characterization of completely connected clustered graphs (where each subgraph induced by a cluster and its complement are connected) [1]: A completely connected clustered graph is c-planar if and only if the underlying graph is planar. More results on c-planarity can be found in [2].…”

Section: Introductionmentioning

confidence: 99%

Clustered Planarity: Clusters with Few Outgoing Edges

et al. 2009

View full text Add to dashboard Cite

show abstract

“…We refer to [5] for basic definitions about graphs and embeddings, and to [8,4,11,3,10,1,6,2,13,12] for basic definitions about clustered graphs and c-planar drawings.…”

Section: Introductionmentioning

confidence: 99%

“…Restrictions on the c-planarity testing problem that have been considered in the literature include: (i) assuming that each cluster induces a small number of connected components [8,4,11,10,1,2,12] (in particular, the case in which the graph is c-connected, that is, each cluster induces one connected component, has been deeply investigated); (ii) considering only flat hierarchies, where all clusters different from the root of T are children of the root [3,6]; (iii) focusing on particular families of underlying graphs [3,13]; and (iv) fixing the embedding of the underlying graph [6,12].…”

mentioning

confidence: 99%

Splitting Clusters to Get C-Planarity

2010

View full text Add to dashboard Cite

Abstract. In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the SPLIT-C-PLANARITY problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that SPLIT-C-PLANARITY is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected seriesparallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters.

show abstract

Completely connected clustered graphs

Cited by 36 publications

References 15 publications

Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces

Efficient C-Planarity Testing for Embedded Flat Clustered Graphs with Small Faces

Clustered Planarity: Clusters with Few Outgoing Edges

Splitting Clusters to Get C-Planarity

Contact Info

Product

Resources

About