A Note on Off-Diagonal Small On-Line Ramsey Numbers for Paths

Abstract

In this note, we consider the on-line Ramsey numbers $\overline{R}(P_n,P_m)$ for paths. Using a high-performance computing cluster, we calculated the values for off-diagonal numbers for paths of lengths at most $8$. Also, we were able to check that $\overline{R}(P_9,P_9)=17$, thus solving the problem raised in [5].