A note on off-diagonal small on-line Ramsey numbers for paths. (English) Zbl 1289.05333
Summary: In this note we consider the on-line Ramsey numbers \(\overline {\mathcal {R}}(P_n,P_m)\) for paths. Using a high performance computing cluster, we calculated the values for off-diagonal numbers for paths of lengths at most 8. We were also able to check that \(\overline {\mathcal {R}}(P_9,P_9)=17\), thus solving the problem raised in the author’s paper [Australas. J. Comb. 40, 27–36 (2008; Zbl 1141.05061)].
MSC:
05C55 | Generalized Ramsey theory |
05C57 | Games on graphs (graph-theoretic aspects) |
91A05 | 2-person games |