The exact multicolour matching Ramsey number R_s(t) for s-connectors is sum_j (t_j - 1) + max{2s, s + max_j t_j}.
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An exact robust Ramsey theorem for matchings
The exact multicolour matching Ramsey number R_s(t) for s-connectors is sum_j (t_j - 1) + max{2s, s + max_j t_j}.