Ramsey Numbers of Connected Clique Matchings

  • Barnaby Roberts
Keywords: Graph theory, Ramsey theory

Abstract

We determine the Ramsey number of a connected clique matching. That is, we show that if $G$ is a $2$-edge-coloured complete graph on $(r^2-r-1)n-r+1$ vertices, then there is a monochromatic connected subgraph containing $n$ disjoint copies of $K_r$, and that this number of vertices cannot be reduced.

Published
2017-02-17
Article Number
P1.36