We show an algorithm to construct a greedy drawing of every given triangulation. The algorithm relies on two main results. First, we show how to construct greedy drawings of a fairly simple class of graphs, called triangulated binary cactuses. Second, we show that every triangulation can be spanned by a triangulated binary cactus. Further, we discuss how to extend our techniques in order to prove that every triconnected planar graph admits a greedy drawing. Such a result, which proves a conjecture by Papadimitriou and Ratajczak, was independently shown by Leighton and Moitra.

An Algorithm to Construct Greedy Drawings of Triangulations

GRILLI, LUCA
2010

Abstract

We show an algorithm to construct a greedy drawing of every given triangulation. The algorithm relies on two main results. First, we show how to construct greedy drawings of a fairly simple class of graphs, called triangulated binary cactuses. Second, we show that every triangulation can be spanned by a triangulated binary cactus. Further, we discuss how to extend our techniques in order to prove that every triconnected planar graph admits a greedy drawing. Such a result, which proves a conjecture by Papadimitriou and Ratajczak, was independently shown by Leighton and Moitra.
2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/129644
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