Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs

Alexei Lisitsa; Viktor Lopatkin; Alexei Vernitski

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arXiv · 2212.07140

Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs

Alexei Lisitsa·Viktor Lopatkin·Alexei Vernitski

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Abstract

Two recent publications describe realizable Gauss diagrams using conditions stating that the number of chords in certain sets of chords is even or odd. We demonstrate that these descriptions are incorrect by finding multiple counter-examples. However, the idea of having a parity-based description of realizable Gauss diagrams is attractive. We recall that realizability of Gauss diagrams as touch curves can be described via bipartite graphs. We show that realizable Gauss diagrams can be described via bipartite graphs.

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BibTeX RIS

Alexei Lisitsa, Viktor Lopatkin, Alexei Vernitski. 2022-12-14. Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs. https://arxiv.org/abs/2212.07140

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