Edge-constrained Hamiltonian paths on a point set LNCS Antić, Todor Džuklevski, Aleksa Fiala, Jiří Kratochvíl, Jan Liotta, Giuseppe Saghafian, Morteza Saumell, Maria Zink, Johannes 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 Nature 2026 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/21374 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-032-17801-5_39 info:eu-repo/semantics/altIdentifier/issn/0302-9743 info:eu-repo/semantics/altIdentifier/e-issn/1611-3349 info:eu-repo/semantics/altIdentifier/isbn/9783032178008 info:eu-repo/semantics/altIdentifier/arxiv/2511.22526 info:eu-repo/semantics/openAccess