Comparing expressive powers of forbidden orientations and edge-colourings

Determine whether the expressive powers of forbidden orientations and forbidden 2-edge-coloured graphs are incomparable; that is, determine whether each formalism expresses graph classes that the other does not.

Background

The paper places forbidden 2-edge-colouring in the broader study of equipped graphs and compares it with earlier work on forbidden orientations. It explicitly asks whether the two formalisms are incomparable, meaning that neither one subsumes the expressive power of the other.

References

We ask if the expressive power of forbidden orientations and of forbidden 2-edge-coloured graphs are incomparable, i.e., are there graph classes expressible by forbidden orientations and not by forbidden 2-edge-coloured graphs? (and vice versa).

— On the expressive power of $2$-edge-colourings of graphs  (2503.07409 - Bok et al., 10 Mar 2025) in Section 10, Conclusions