Ramsey numbers of connected clique matchings

Roberts, B. (2017). Ramsey numbers of connected clique matchings. Electronic Journal of Combinatorics, 24(1), P1.36.
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We determine the Ramsey number of a connected clique matching. That is, we show that if GG is a 22-edge-coloured complete graph on (r2−r−1)n−r+1(r2−r−1)n−r+1 vertices, then there is a monochromatic connected subgraph containing nn disjoint copies of KrKr, and that this number of vertices cannot be reduced.

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