Lisitsa, Alexei and Lopatkin, Viktor and Vernitski, Alexei (2023) Describing realizable gauss diagrams using the concepts of parity or bipartite graphs. Journal of Knot Theory and Its Ramifications, 32 (10). DOI https://doi.org/10.1142/S0218216523500591
Lisitsa, Alexei and Lopatkin, Viktor and Vernitski, Alexei (2023) Describing realizable gauss diagrams using the concepts of parity or bipartite graphs. Journal of Knot Theory and Its Ramifications, 32 (10). DOI https://doi.org/10.1142/S0218216523500591
Lisitsa, Alexei and Lopatkin, Viktor and Vernitski, Alexei (2023) Describing realizable gauss diagrams using the concepts of parity or bipartite graphs. Journal of Knot Theory and Its Ramifications, 32 (10). DOI https://doi.org/10.1142/S0218216523500591
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.
Item Type: | Article |
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Uncontrolled Keywords: | Realization of Gauss diagrams; plane curves; parity condition; circle graphs; interlacement graphs |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 26 Jul 2023 11:45 |
Last Modified: | 30 Oct 2024 21:19 |
URI: | http://repository.essex.ac.uk/id/eprint/36056 |
Available files
Filename: Gauss_realizability_July_2023 (1).pdf