On Hamiltonian alternating cycles and paths
Abstract
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. Among them, we prove that a 1-plane Hamiltonian alternating cycle on a bicolored point set in general position can always be obtained, and that when the point set is in convex position, every Hamiltonian alternating cycle with minimum number of crossings is 1-plane. Further, for point sets in convex position, we provide and time algorithms for computing, respectively, Hamiltonian alternating cycles and paths with minimum number of crossings.
Cite
@article{arxiv.1603.06764,
title = {On Hamiltonian alternating cycles and paths},
author = {Mercè Claverol and Alfredo García and Delia Garijo and Carlos Seara and Javier Tejel},
journal= {arXiv preprint arXiv:1603.06764},
year = {2017}
}