Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs
Geometric Topology
2022-12-15 v1
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.
Cite
@article{arxiv.2212.07140,
title = {Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs},
author = {Alexei Lisitsa and Viktor Lopatkin and Alexei Vernitski},
journal= {arXiv preprint arXiv:2212.07140},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2108.02873