Complete expressive-power classification for three-vertex patterns

List all hereditary graph classes expressed by a set of 2-edge-coloured graphs on three vertices.

Background

The paper completely characterizes the classes expressed by patterns on three vertices with at most two edges and also analyzes sets containing both monochromatic paths. It does not provide a complete classification for all sets of three-vertex 2-edge-coloured patterns, so it asks for an exhaustive list of the graph classes obtainable in this way.

References

Problem 49. List all graph classes expressed by a set of 2-edge-coloured-graphs on three vertices.

— On the expressive power of $2$-edge-colourings of graphs  (2503.07409 - Bok et al., 10 Mar 2025) in Problem 49, Section 10, Conclusions