### 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 403-415 |

Number of pages | 13 |

Volume | 9644 |

ISBN (Print) | 9783662495285 |

DOIs | |

State | Published - 2016 |

Event | 12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico Duration: Apr 11 2016 → Apr 15 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 9644 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 12th Latin American Symposium on Theoretical Informatics, LATIN 2016 |
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Country | Mexico |

City | Ensenada |

Period | 4/11/16 → 4/15/16 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - On the planar split thickness of graphs

AU - Eppstein, David

AU - Kindermann, Philipp

AU - Kobourov, Stephen G

AU - Liotta, Giuseppe

AU - Lubiw, Anna

AU - Maignan, Aude

AU - Mondal, Debajyoti

AU - Vosoughpour, Hamideh

AU - Whitesides, Sue

AU - Wismath, Stephen

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84961683199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961683199&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-49529-2_30

DO - 10.1007/978-3-662-49529-2_30

M3 - Conference contribution

AN - SCOPUS:84961683199

SN - 9783662495285

VL - 9644

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 403

EP - 415

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -