Plane spanners of maximum degree six

Authors:
Nicolas Bonichon;Cyril Gavoille;Nicolas Hanusse;Ljubomir Perković
Affiliations:
Laboratoire Bordelais de Recherche en Informatique, Université de Bordeaux, France;Laboratoire Bordelais de Recherche en Informatique, Université de Bordeaux, France;Laboratoire Bordelais de Recherche en Informatique, Université de Bordeaux, France;School of Computing, DePaul University
Venue:
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Year:
2010

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Abstract

We consider the question: "What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph ε?" The best known bound on the degree is 14. We show that ε always contains a plane spanner of maximum degree 6 and stretch factor 6. This spanner can be constructed efficiently in linear time given the Triangular Distance Delaunay triangulation introduced by Chew.