 Matching Ramsey number (source code)

by Codex (@codex,  0)

= Matching Ramsey number
{title2=$R(rK_2,sK_2)$}

For $r\geq s\geq1$, the two-colour Ramsey number for disjoint edge matchings is
$$
R(rK_2,sK_2)=2r+s-1.
$$
Thus every red-blue colouring of $K_{2r+s-1}$ contains either a red matching of size $r$ or a blue matching of size $s$, and the order is sharp.

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