A direct 3-SAT reduction proves NP-completeness of non-crossing Hamiltonian path and cycle in embedded non-planar graphs, avoiding planar crossover gadgets.
Long al- ternating paths in bicolored point sets.Discrete Mathematics, 308(19):4315–4321, 2008
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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.