Skip to Main content Skip to Navigation
Conference papers

Every Collinear Set in a Planar Graph Is Free

Abstract : We show that if a planar graph G has a plane straight-line drawing in which a subset S of its vertices are collinear, then for any set of points, X, in the plane with |X| = |S|, there is a plane straight-line drawing of G in which the vertices in S are mapped to the points in X. This solves an open problem posed by Ravsky and Verbitsky in 2008. In their terminology, we show that every collinear set is free. This result has applications in graph drawing, including untangling, column pla- narity, universal point subsets, and partial simultaneous drawings.
Document type :
Conference papers
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download
Contributor : Daniel Gonçalves Connect in order to contact the contributor
Submitted on : Friday, March 8, 2019 - 9:13:35 AM
Last modification on : Monday, October 11, 2021 - 1:24:08 PM
Long-term archiving on: : Monday, June 10, 2019 - 10:53:43 AM


1811.03432 (1).pdf
Files produced by the author(s)




Vida Dujmović, Fabrizio Frati, Daniel Gonçalves, Pat Morin, Günter Rote. Every Collinear Set in a Planar Graph Is Free. SODA: Symposium on Discrete Algorithms, Jan 2019, San Diego, CA, United States. pp.1521-1538, ⟨10.1137/1.9781611975482.92⟩. ⟨lirmm-02046476⟩



Record views


Files downloads