Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs
arXiv (Cornell University)(2023)
摘要
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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关键词
hamiltonian cycles,simple drawings,crossing-free
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