Edge-ordered Ramsey numbers of complete graphs

Determine whether the exponential lower bound for edge-ordered Ramsey numbers of arbitrarily ordered complete graphs K_n is tight.

Background

The survey identifies finding a better estimate for edge-ordered Ramsey numbers of edge-ordered complete graphs as a major open question. In particular, it records the question of whether the known exponential lower bound is tight for general edge orderings.

References

For edge-ordered graphs, a major open question is to find a better estimate for edge-ordered Ramsey numbers of edge-ordered complete graphs on $n$ vertices. In particular, Fox and Li asked whether the exponential lower bound is tight for general edge-orderings of $K_n$.

— A Survey on Ordered Ramsey Numbers  (2502.02155 - Balko, 4 Feb 2025) in Section 4, paragraph beginning “For edge-ordered graphs, a major open question”