NP-completeness of mutual-visibility coloring

A graph $G$ has a mutual-visibility coloring if its vertices can be colored so that the required mutual-visibility condition holds; the associated decision problem asks whether $G$ admits such a coloring with a prescribed number of colors.

Mutual-visibility coloring conjecture. The mutual-visibility coloring decision problem is NP-complete.

The paper proves NP-completeness for the independent version, even for graphs with universal vertices, and conjectures that the same computational complexity holds for the basic version.