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### Untangling planar graphs from a specified vertex position — hard cases

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Kang, Minkyung, Pikhurko, Oleg, Ravsky, A., Schacht, M. and Verbitsky, O..
(2011)
*Untangling planar graphs from a specified vertex position — hard cases.*
Discrete Applied Mathematics, Vol.159
(No.8).
pp. 789-799.
ISSN 0166-218X

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1016/j.dam.2011.01.011

## Abstract

Given a planar graph G, we consider drawings of G in the plane where edges are represented by straight line segments (which possibly intersect). Such a drawing is specified by an injective embedding π of the vertex set of G into the plane. Let be the maximum integer k such that there exists a crossing-free redrawing π′ of G which keeps k vertices fixed, i.e., there exist k vertices v1,…,vk of G such that π(vi)=π′(vi) for i=1,…,k. Given a set of points X, let denote the value of minimized over π locating the vertices of G on X. The absolute minimum of is denoted by .

For the wheel graph Wn, we prove that for every X. With a somewhat worse constant factor this is also true for the fan graph Fn. We inspect also other graphs for which it is known that .

We also show that the minimum value of the parameter is always attainable by a collinear X.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Mathematics |

Journal or Publication Title: | Discrete Applied Mathematics |

Publisher: | Elsevier Science Ltd. |

ISSN: | 0166-218X |

Official Date: | 28 April 2011 |

Volume: | Vol.159 |

Number: | No.8 |

Page Range: | pp. 789-799 |

Identification Number: | 10.1016/j.dam.2011.01.011 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

URI: | http://wrap.warwick.ac.uk/id/eprint/43842 |

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