Paths with no Small Angles
نویسندگان
چکیده
Giving a (partial) solution to a problem of S. Fekete [3] and S. Fekete and G.J. Woeginger [4] we show that given a finite set X of points in the plane, it is possible to find a polygonal path with |X|−1 segments and with 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. We show further that the same result holds, with an angle smaller than π/9, in higher dimensions.
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 23 شماره
صفحات -
تاریخ انتشار 2008