conference paper published yes Todor Antić author Aleksa Džuklevski author Jiří Fiala author Jan Kratochvíl author Giuseppe Liotta author Morteza Saghafian author f86f7148-b140-11ec-9577-95435b8df824 Maria Saumell author Johannes Zink author HeEd department SOFSEM: Conference on Current Trends in Theory and Practice of Computer Science Let . S be a set of distinct points in general position in the Euclidean plane. A plane Hamiltonian path on . S is a crossing-free geometric path such that every point of .S is a vertex of the path. It is known that, if. S is sufficiently large, there exist three edge-disjoint plane Hamiltonian paths on . S. In this paper we study an edge-constrained version of the problem of finding Hamiltonian paths on a point set. We first consider the problem of finding a single plane Hamiltonian path . π with endpoints .s, t ∈ S and constraints given by a segment . ab, where .a, b ∈ S. We consider the following scenarios: (i) .ab ∈ π; (ii) .ab π. We characterize those quintuples . S, a, b, s, t for which . π exists. Secondly, we consider the problem of finding two plane Hamiltonian paths . π1, π2 on a set . S with constraints given by a segment . ab, where .a, b ∈ S. We consider the following scenarios: (i) .π1 and .π2 share no edges and .ab is an edge of . π1; (ii) .π1 and .π2 share no edges and none of them includes .ab as an edge; (iii) both .π1 and .π2 include .ab as an edge and share no other edges. In all cases, we characterize those triples . S, a, b for which .π1 and .π2 exist. Springer Nature2026Krakow, Poland eng 0302-9743 1611-3349 9783032178008 2511.2252610.1007/978-3-032-17801-5_39 16448532-546 Antić, T., Džuklevski, A., Fiala, J., Kratochvíl, J., Liotta, G., Saghafian, M., … Zink, J. (2026). Edge-constrained Hamiltonian paths on a point set. In <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i> (Vol. 16448, pp. 532–546). Krakow, Poland: Springer Nature. <a href="https://doi.org/10.1007/978-3-032-17801-5_39">https://doi.org/10.1007/978-3-032-17801-5_39</a> Antić, Todor, et al. “Edge-Constrained Hamiltonian Paths on a Point Set.” <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, vol. 16448, Springer Nature, 2026, pp. 532–46, doi:<a href="https://doi.org/10.1007/978-3-032-17801-5_39">10.1007/978-3-032-17801-5_39</a>. T. Antić <i>et al.</i>, “Edge-constrained Hamiltonian paths on a point set,” in <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, Krakow, Poland, 2026, vol. 16448, pp. 532–546. Antić, Todor, Aleksa Džuklevski, Jiří Fiala, Jan Kratochvíl, Giuseppe Liotta, Morteza Saghafian, Maria Saumell, and Johannes Zink. “Edge-Constrained Hamiltonian Paths on a Point Set.” In <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>, 16448:532–46. Springer Nature, 2026. <a href="https://doi.org/10.1007/978-3-032-17801-5_39">https://doi.org/10.1007/978-3-032-17801-5_39</a>. Antić T, Džuklevski A, Fiala J, Kratochvíl J, Liotta G, Saghafian M, Saumell M, Zink J. 2026. Edge-constrained Hamiltonian paths on a point set. 51st International Conference on Current Trends in Theory and Practice of Computer Science. SOFSEM: Conference on Current Trends in Theory and Practice of Computer Science, LNCS, vol. 16448, 532–546. Antić T, Džuklevski A, Fiala J, et al. Edge-constrained Hamiltonian paths on a point set. In: <i>51st International Conference on Current Trends in Theory and Practice of Computer Science</i>. Vol 16448. Springer Nature; 2026:532-546. doi:<a href="https://doi.org/10.1007/978-3-032-17801-5_39">10.1007/978-3-032-17801-5_39</a> T. Antić, A. Džuklevski, J. Fiala, J. Kratochvíl, G. Liotta, M. Saghafian, M. Saumell, J. Zink, in:, 51st International Conference on Current Trends in Theory and Practice of Computer Science, Springer Nature, 2026, pp. 532–546. 213742026-03-01T23:01:40Z2026-03-02T08:49:20Z