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Hamiltonian path problem remains NP-complete in planar graphs [1], so your problem is also NP-complete since in a planar graph, two edges cannot intersect with each other. [1] Garey, M. R., Johnson, D. S., & Tarjan, R. E. (1976). The planar Hamiltonian circuit problem is NP-complete. SIAM Journal on Computing, 5(4), 704-714.


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