Publication: A note on small on-line Ramsey numbers for paths and their generalization
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A note on small on-line Ramsey numbers for paths and their generalization
||Australasian Journal of Combinatorics
||In this note, we consider the on-line Ramsey numbers R(P_n) for paths and their generalization. The standard on-line Ramsey game is played on an unbounded set of vertices, whereas the new variant of the game we consider is the game where the number of vertices is bounded. Using a computer cluster, we âcalculatedâ some new values for short paths, both for the generalized on-line Ramsey numbers and the classical ones. In particular, we showed that R(P_7)=12, R(P_8)=15, and R(P_9) \le 17.
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