Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs
DOI:
https://doi.org/10.57717/cgt.v3i2.47Abstract
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.
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Copyright (c) 2023 Oswin Aichholzer, Joachim Orthaber, Birgit Vogtenhuber
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