@article{Aichholzer_Orthaber_Vogtenhuber_2024, title={Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs}, volume={3}, url={https://cgt-journal.org/index.php/cgt/article/view/47}, DOI={10.57717/cgt.v3i2.47}, abstractNote={<p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">It is a longstanding conjecture that every simple drawing of a complete graph on n ≥ 3 vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to “there exists a crossing-free Hamiltonian path between each pair of vertices” and show that this stronger conjecture holds for several classes of simple drawings, including strongly c-monotone drawings and cylindrical drawings. As a second main contribution, we give an overview on different classes of simple drawings and investigate inclusion relations between them up to weak isomorphism.</p>}, number={2}, journal={Computing in Geometry and Topology}, author={Aichholzer, Oswin and Orthaber, Joachim and Vogtenhuber, Birgit}, year={2024}, month={Jan.}, pages={5:1–5:30} }