Every Collinear Set in a Planar Graph Is Free - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Conference Papers Year : 2019

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.

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Discrete Mathematics [cs.DM]
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Submitted on : Friday, March 8, 2019-9:13:35 AM

Last modification on : Wednesday, July 12, 2023-1:43:14 PM

Long-term archiving on : Monday, June 10, 2019-10:53:43 AM

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lirmm-02046476 , version 1 (08-03-2019)

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Vida Dujmović, Fabrizio Frati, Daniel Gonçalves, Pat Morin, Günter Rote. Every Collinear Set in a Planar Graph Is Free. SODA 2019 - 30th Annual ACM-SIAM Symposium on Discrete Algorithms, Jan 2019, San Diego, CA, United States. pp.1521-1538, ⟨10.1137/1.9781611975482.92⟩. ⟨lirmm-02046476⟩

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