Abstract
We consider the question: “What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph \(\mathcal E\)?” The best known bound on the degree is 14. We show that \(\mathcal E\) 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.
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Bonichon, N., Gavoille, C., Hanusse, N., Perković, L. (2010). Plane Spanners of Maximum Degree Six. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_3
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DOI: https://doi.org/10.1007/978-3-642-14165-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14164-5
Online ISBN: 978-3-642-14165-2
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