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: Contribution to journalArticle

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 graphs, complete bipartite graphs, multipartite graphs, bounded degree graphs, and genus-1 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-splittability in linear time, for a constant k.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalAlgorithmica
DOIs
StateAccepted/In press - Jun 2 2017

Fingerprint

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

Keywords

  • Approximation
  • Complete graphs
  • Fixed-parameter tractable
  • Genus-1 graphs
  • Graph drawing
  • Graph theory
  • NP-hardness
  • Planarity
  • Splittable
  • Thickness

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

Eppstein, D., Kindermann, P., Kobourov, S. G., Liotta, G., Lubiw, A., Maignan, A., ... Wismath, S. (Accepted/In press). On the Planar Split Thickness of Graphs. Algorithmica, 1-18. https://doi.org/10.1007/s00453-017-0328-y

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.

In: Algorithmica, 02.06.2017, p. 1-18.

Research output: Contribution to journalArticle

Eppstein, D, Kindermann, P, Kobourov, SG, Liotta, G, Lubiw, A, Maignan, A, Mondal, D, Vosoughpour, H, Whitesides, S & Wismath, S 2017, 'On the Planar Split Thickness of Graphs', Algorithmica, pp. 1-18. https://doi.org/10.1007/s00453-017-0328-y
Eppstein D, Kindermann P, Kobourov SG, Liotta G, Lubiw A, Maignan A et al. On the Planar Split Thickness of Graphs. Algorithmica. 2017 Jun 2;1-18. https://doi.org/10.1007/s00453-017-0328-y
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. In: Algorithmica. 2017 ; pp. 1-18.
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