Abstract: Given a graph H, the Ramsey number is the smallest positive integer n such that every 2-edge-colouring of yields a monochromatic copy of . We write to denote the union of vertex-disjoint copies of . The members of the family  are also known as -tilings. A well-known result of Burr, Erdős and Spencer states that for every . On the other hand, Moon proved that every 2-edge-colouring of  yields a -tiling consisting of monochromatic copies of , for every . Crucially, in Moon's result, distinct copies of   might receive different colours. In this talk, we investigate the analogous questions where the complete host graph is replaced by a graph of large minimum degree and generalise both Moon's theorem and the Burr--Erdős--Spencer  theorem to this setting. This is joint work with József Balogh and Andrea Freschi.