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

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