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Bicolored point sets admitting non-crossing alternating Hamiltonian paths
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abstract
Consider a bicolored point set $P$ in general position in the plane consisting of $n$ blue and $n$ red points. We show that if a subset of the red points forms the vertices of a convex polygon separating the blue points, lying inside the polygon, from the remaining red points, lying outside the polygon, then the points of $P$ can be connected by non-crossing straight-line segments so that the resulting graph is a properly colored closed Hamiltonian path.
Forward citations
Cited by 2 Pith papers
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On plane cycles in geometric multipartite graphs
New bounds and an FPT algorithm for plane cycles in geometric bipartite graphs, but the main characterization theorem is refuted by a four-point counterexample.
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NP-Hardness of Non-Crossing Hamiltonian Path and Cycle in Non-Planar Graphs
A direct 3-SAT reduction proves NP-completeness of non-crossing Hamiltonian path and cycle in embedded non-planar graphs, avoiding planar crossover gadgets.
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