Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909252136730624 |
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| author | Vernitski, Alexei |
| author_facet | Vernitski, Alexei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters Vernitski, Alexei Geometric Topology General Topology 57K10 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. |
| title | Gauss diagrams as cubic graphs: The choice of the Hamiltonian cycle matters |
| topic | Geometric Topology General Topology 57K10 |
| url | https://arxiv.org/abs/2407.09144 |