Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters

Alexei Vernitski

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arXiv · 2407.09144

Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters

Alexei Vernitski

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Abstract

We explore to what extent the properties of a Gauss diagram are affected by the choice of its Hamiltonian cycle. We present an example of a realizable Gauss diagram and an unrealizable Gauss diagram that differ only by a choice of the Hamiltonian cycle. We present an example of two Gauss diagrams that correspond to different curves and differ only by a choice of the Hamiltonian cycle. We prove that a certain natural type of change of the Hamiltonian cycle preserves the realizability of the Gauss diagram.

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Alexei Vernitski. 2024-07-12. Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters. https://arxiv.org/abs/2407.09144

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