The Library
Untangling planar graphs from a specified vertex position — hard cases
Tools
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. doi:10.1016/j.dam.2011.01.011 ISSN 0166-218X.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
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, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Discrete Applied Mathematics | ||||
Publisher: | Elsevier Science Ltd. | ||||
ISSN: | 0166-218X | ||||
Official Date: | 28 April 2011 | ||||
Dates: |
|
||||
Volume: | Vol.159 | ||||
Number: | No.8 | ||||
Page Range: | pp. 789-799 | ||||
DOI: | 10.1016/j.dam.2011.01.011 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |