Monochromatic connected matchings in almost complete graphs

Shoham Letzter

Published 2020-09-07Version 1

A connected matching in a graph $G$ is a matching that is contained in a connected component of $G$. A well-known method due to {\L}uczak reduces problems about monochromatic paths and cycles in complete graphs to problems about monochromatic matchings in almost complete graphs. We show that these can be further reduced to problems about monochromatic connected matchings in complete graphs.