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A connected matching in a graph $G$ is a matching contained in a connectedcomponent of $G$. A well-known method due to {\L}uczak reduces problems aboutmonochromatic paths and cycles in complete graphs to problems aboutmonochromatic connected matchings in almost complete graphs. We show that thesecan be further reduced to problems about monochromatic connected matchings incomplete graphs.  We illustrate the potential of this new reduction by showing how it can beused to determine the $3$-colour Ramsey number of long paths, using a simplerargument than the original one by Gy\'arf\'as, Ruszink\'o, S\'ark\"ozy, andSzemer\'edi (2007).

An improvement on {\L}uczak's connected matchings method