Drawing Hamiltonian Cycles with No Large AnglesDumitrescu, Adrian and Pach, János and Tóth, Géza (2010) Drawing Hamiltonian Cycles with No Large Angles. In: Graph Drawing 17th International Symposium, GD 2009, September 2225, 2009 , pp. 314(Official URL: http://dx.doi.org/10.1007/9783642118050_3). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783642118050_3
AbstractLet n ≥ 4 be even. It is shown that every set S of n points in the plane can be connected by a (possibly selfintersecting) spanning tour (Hamiltonian cycle) consisting of n straight line edges such that the angle between any two consecutive edges is at most 2π/3. For n = 4 and 6, this statement is tight. It is also shown that every evenelement point set S can be partitioned into at most two subsets, S1 and S2 , each admitting a spanning tour with no angle larger than π/2. Fekete and Woeginger conjectured that for suﬃciently large even n, every nelement set admits such a spanning tour. We conﬁrm this conjecture for point sets in convex position. A much stronger result holds for large point sets randomly and uniformly selected from an open region bounded by ﬁnitely many rectiﬁable curves: for any ε > 0, these sets almost surely admit a spanning tour with no angle larger than ε.
Actions (login required)
