Untangling planar graphs from a specified vertex position — hard cases
Kang, M., 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 0166-218XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.dam.2011.01.011
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.|
|Official Date:||28 April 2011|
|Page Range:||pp. 789-799|
|Access rights to Published version:||Restricted or Subscription Access|
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