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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. 789799. ISSN 0166218X
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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 crossingfree 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:  0166218X  
Official Date:  28 April 2011  
Dates: 


Volume:  Vol.159  
Number:  No.8  
Page Range:  pp. 789799  
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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