For a set of positive integers A⊆[n], an r-coloring of A is rainbow sum-free if it contains no
rainbow Schur triple. In this paper we initiate the study of the rainbow Erdős-Rothschild …

The canonical van der Waerden theorem states that, for large enough n, any colouring of [n]
gives rise to monochromatic or rainbow k-APs. In this work, we are interested in sparse …