[HTML][HTML] On Hamiltonian alternating cycles and paths
Computational Geometry, 2018•Elsevier
We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored
point sets. This has been an intensively studied problem, not always with a solution, when
the paths and cycles are also required to be plane. In this paper, we relax the constraint on
the cycles and paths from being plane to being 1-plane, and deal with the same type of
questions as those for the plane case, obtaining a remarkable variety of results. For point
sets in general position, our main result is that it is always possible to obtain a 1-plane …
point sets. This has been an intensively studied problem, not always with a solution, when
the paths and cycles are also required to be plane. In this paper, we relax the constraint on
the cycles and paths from being plane to being 1-plane, and deal with the same type of
questions as those for the plane case, obtaining a remarkable variety of results. For point
sets in general position, our main result is that it is always possible to obtain a 1-plane …
We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same type of questions as those for the plane case, obtaining a remarkable variety of results. For point sets in general position, our main result is that it is always possible to obtain a 1-plane Hamiltonian alternating cycle. When the point set is in convex position, we prove that every Hamiltonian alternating cycle with minimum number of crossings is 1-plane, and provide O (n) and O (n 2) time algorithms for computing, respectively, Hamiltonian alternating cycles and paths with minimum number of crossings.
Elsevier
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