Improving the upper bound for the K5 target

Improve the known upper bound for L(K_n,K_5) substantially beyond \(\left(\frac{3}{4}+o(1)\right)\binom{n}{2}\), or otherwise resolve the open problem of determining significantly smaller asymptotic bounds.

Background

For the strong Ramsey game with target K_5 on the complete board K_n, the paper records the upper bound L(K_n,K_5)\le \left(\frac{3}{4}+o(1)\right)\binom{n}{2}. This is far from the bounded-move behavior conjectured for complete-graph targets.

The concluding remarks explicitly identify substantial improvement of this bound as an unresolved problem, making it a concrete special case of the broader bounded-move conjecture.