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.
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References
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© 2008 Springer-Verlag Berlin Heidelberg
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Bárány, I., Pór, A., Valtr, P. (2008). Paths with no Small Angles. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_56
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DOI: https://doi.org/10.1007/978-3-540-78773-0_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78772-3
Online ISBN: 978-3-540-78773-0
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