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

4 Scopus citations

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

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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., Mondal, D., Vosoughpour, H., Whitesides, S., & Wismath, S. (Accepted/In press). On the Planar Split Thickness of Graphs. Algorithmica, 1-18. https://doi.org/10.1007/s00453-017-0328-y