International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 348-359 | Cite as

Drawing Graphs with Vertices and Edges in Convex Position

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

A graph has strong convex dimension 2, if it admits a straight-line drawing in the plane such that its vertices are in convex position and the midpoints of its edges are also in convex position. Halman, Onn, and Rothblum conjectured that graphs of strong convex dimension 2 are planar and therefore have at most \(3n-6\) edges. We prove that all such graphs have at most \(2n-3\) edges while on the other hand we present a class of non-planar graphs of strong convex dimension 2. We also give lower bounds on the maximum number of edges a graph of strong convex dimension 2 can have and discuss variants of this graph class. We apply our results to questions about large convexly independent sets in Minkowski sums of planar point sets, that have been of interest in recent years.

References

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LIPENS Lyon - CNRS - UCBL - INRIA, Université de Lyon UMR 5668LyonFrance
  2. 2.Aix-Marseille Université, CNRS, LIF UMR 7279MarseilleFrance

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