Edge-ordered complete graphs

Determine whether the exponential lower bound is tight for general edge-orderings of the complete graph K_n by obtaining a matching upper bound for its edge-ordered Ramsey number.

Background

The survey identifies finding better estimates 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 asymptotically tight for arbitrary 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 Discussion preceding Conjecture prob-ordRamHyper-edgeDegen, Section “Edge-ordered Ramsey Numbers”