On the planar split thickness of graphs

David Eppstein, Philipp Kindermann, Stephen G Kobourov, Giuseppe Liotta, Anna Lubiw, Aude Maignan, Debajyoti Mondal, Hamideh Vosoughpour, Sue Whitesides, Stephen Wismath

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest k such that the graph is k-splittable into a planar graph. A k-split operation substitutes a vertex v by at most k new vertices such that each neighbor of v is connected to at least one of the new vertices. We first examine the planar split thickness of complete and complete bipartite graphs. We then prove that it is NP-hard to recognize graphs that are 2-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify k-splittablity in linear time, for a constant k.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages403-415
Number of pages13
Volume9644
ISBN (Print)9783662495285
DOIs
StatePublished - 2016
Event12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico
Duration: Apr 11 2016Apr 15 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9644
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th Latin American Symposium on Theoretical Informatics, LATIN 2016
CountryMexico
CityEnsenada
Period4/11/164/15/16

Fingerprint

Drawing (graphics)
Visualization
Graph in graph theory
Planar graph
Information Visualization
Graph Drawing
Treewidth
Complete Bipartite Graph
Substitute
Linear Time
NP-complete problem
Verify
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Eppstein, D., Kindermann, P., Kobourov, S. G., Liotta, G., Lubiw, A., Maignan, A., ... Wismath, S. (2016). On the planar split thickness of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9644, pp. 403-415). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_30

On the planar split thickness of graphs. / Eppstein, David; Kindermann, Philipp; Kobourov, Stephen G; Liotta, Giuseppe; Lubiw, Anna; Maignan, Aude; Mondal, Debajyoti; Vosoughpour, Hamideh; Whitesides, Sue; Wismath, Stephen.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9644 Springer Verlag, 2016. p. 403-415 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Eppstein, D, Kindermann, P, Kobourov, SG, Liotta, G, Lubiw, A, Maignan, A, Mondal, D, Vosoughpour, H, Whitesides, S & Wismath, S 2016, On the planar split thickness of graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9644, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9644, Springer Verlag, pp. 403-415, 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, Ensenada, Mexico, 4/11/16. https://doi.org/10.1007/978-3-662-49529-2_30
Eppstein D, Kindermann P, Kobourov SG, Liotta G, Lubiw A, Maignan A et al. On the planar split thickness of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9644. Springer Verlag. 2016. p. 403-415. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-49529-2_30
Eppstein, David ; Kindermann, Philipp ; Kobourov, Stephen G ; Liotta, Giuseppe ; Lubiw, Anna ; Maignan, Aude ; Mondal, Debajyoti ; Vosoughpour, Hamideh ; Whitesides, Sue ; Wismath, Stephen. / On the planar split thickness of graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9644 Springer Verlag, 2016. pp. 403-415 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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