Finite forbidden-orientation characterization of co-bipartite graphs

Prove or disprove that no finite set of oriented graphs characterizes the class of co-bipartite graphs.

Background

The paper contrasts the known expressibility results for co-bipartite graphs under forbidden 2-edge-colourings with the unresolved status of analogous descriptions by forbidden orientations. The authors explicitly state their belief that no finite forbidden-orientation characterization exists for co-bipartite graphs.

References

In particular, we believe that there is no finite set of 2-edge-coloured graphs expressing bipartite graphs, and no finite set of oriented graphs characterizing co-bipartite graphs.

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