Drawing planar graphs on points inside a polygon

Authors:
Therese Biedl;Peter Floderus
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Canada;Department of Mathematics, University of Lund, Sweden
Venue:
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Year:
2012

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Abstract

In this paper, we study the problem of drawing a given planar graph such that vertices are at pre-specified points and the entire drawing is inside a given polygon. We give a method that shows that for an n-vertex graph and a k-sided polygon, Θ(kn2) bends are always sufficient. We also give an example of a graph where Θ(kn2) bends are necessary for such a drawing.