2024/01/24 by Aichholzer, Oswin, Orthaber, Joachim, Vogtenhuber, Birgit · 1 citation
paper · doi:10.57717/cgt.v3i2.47
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. Furthermore, we give an overview on different classes of simple drawings and investigate implications between them up to weak isomorphism.