Two-word strict multi-1-11-representation bound

Prove or disprove that the strict multi-1-11-representation number of every graph is at most 2.

Background

The paper proves that every graph on at most 24 vertices has strict multi-1-11-representation number at most 2. It asks whether the same bound holds for arbitrary graphs, independently of whether every graph is itself 1-11-representable.

References

Assuming that proving or disproving that any graph is 1-11-representable remains infeasible with existing tools, one could focus on proving or disproving that the (strict) multi-1-11-representation number of any graph is at most 2.

— On 1-11-representability and multi-1-11-representability of graphs  (2501.13871 - Alshammari et al., 23 Jan 2025) in Section 5, Concluding remarks, page 9