Paths with no small angles

Authors:
Imre Bárány;Attila Pór;Pavel Valtr
Affiliations:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary and Department of Mathematics, University College London, London, England;Department of Applied Mathematics, Charles University, Praha 1, Czech Republic;Department of Applied Mathematics, Charles University, Praha 1, Czech Republic
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

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Abstract

Giving a partial solution to a problem of S. Fekete and G.J. Woeginger [3,4] we show that given a finite set X of points in the plane, it is possible to arrange them on a polygonal path (with the vertex set X) so that every angle on the polygonal path is at least π/9. According to a conjecture of Fekete and Woeginger, π/9 can be replaced by π/6. Previously, the result has not been known with any positive constant.