Ramsey numbers of path-matchings, covering designs and 1-cores

Louis DeBiasio, András Gyárfás, Gábor N. Sárközy

A path-matching of order $p$ is a vertex disjoint union of nontrivial paths spanning $p$ vertices. Burr and Roberts, and Faudree and Schelp determined the 2-color Ramsey number of…