  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.
