So it can be rendered into LaTeX PDFs more nicely.

Needed so we can produce a novel 2-coloring for the neighborhood of a vertex in a 3-colorable graph. Robustness is needed so we do not need to know anything a priori about the 2-colorability of a graph and can produce either a complete 2-coloring or a proof that the graph is not 2-colorable.

Maybe it would be cleaner to construct the witness (odd cycle) in the negative case but it would be more algorithmically involved.

The different variants are confusing, so check the time and replace them with sauto.

To make in line with M.In.