@inproceedings{21374,
  abstract     = {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.},
  author       = {Antić, Todor and Džuklevski, Aleksa and Fiala, Jiří and Kratochvíl, Jan and Liotta, Giuseppe and Saghafian, Morteza and Saumell, Maria and Zink, Johannes},
  booktitle    = {51st International Conference on Current Trends in Theory and Practice of Computer Science},
  isbn         = {9783032178008},
  issn         = {1611-3349},
  location     = {Krakow, Poland},
  pages        = {532--546},
  publisher    = {Springer Nature},
  title        = {{Edge-constrained Hamiltonian paths on a point set}},
  doi          = {10.1007/978-3-032-17801-5_39},
  volume       = {16448},
  year         = {2026},
}