Hamiltonian Alternating Paths on Bicolored Double-Chains

  • Josef Cibulka
  • Jan Kynčl
  • Viola Mészáros
  • Rudolf Stolař
  • Pavel Valtr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

We find arbitrarily large finite sets S of points in general position in the plane with the following property. If the points of S are equitably 2-colored (i.e., the sizes of the two color classes differ by at most one), then there is a polygonal line consisting of straight-line segments with endpoints in S, which is Hamiltonian, non-crossing, and alternating (i.e., each point of S is visited exactly once, every two non-consecutive segments are disjoint, and every segment connects points of different colors).

We show that the above property holds for so-called double-chains with each of the two chains containing at least one fifth of all the points. Our proof is constructive and can be turned into a linear-time algorithm. On the other hand, we show that the above property does not hold for double-chains in which one of the chains contains at most ≈ 1/29 of all the points.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Josef Cibulka
    • 1
  • Jan Kynčl
    • 2
  • Viola Mészáros
    • 3
    • 4
  • Rudolf Stolař
    • 1
  • Pavel Valtr
    • 2
  1. 1.Department of Applied MathematicsCharles University, Faculty of Mathematics and PhysicsPragueCzech Republic
  2. 2.Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI)Charles University, Faculty of Mathematics and PhysicsPragueCzech Republic
  3. 3.Department of Applied Mathematics and Institute for Theoretical Computer ScienceCharles UniversityPragueCzech Republic
  4. 4.Bolyai InstituteUniversity of SzegedSzegedHungary

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