Gieles et al.2018). In these scenarios, the amount of accreted material would depend on the stellar mass.

Our work shows that the oxygen variation needed to reproduce the observed colors of multiple MSs of low-mass stars is consistent with the range of \[O/Fe\] inferred from spectroscopy of more-massive RGB stars. As a consequence, in any scenario based on accretion onto already-existing stars, the rate of accreated material should be proportional to the stellar mass. As an example, our results exclude a Bondi accretion, where the amount of accreted material is proportional to the square of the stellar mass and low-mass stars would be inefficient to accreate polluted material. In general, the discovery of multiple MSs of faint MS stars in NGC6752, together with similar findings on NGC2808, M4 and $\omega$Cen, indicate that multiple sequences of M-dwarfs are common features of GCs. The evidence that stellar populations with different chemical compositions are also present in M-dwarfs, which are fully-convective stars, demonstrates that the chemical composition of multiple populations is not a product of stellar evolution.

acknowledgments {#acknowledgments .unnumbered}
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We thank the referee for her/his work that improved the manuscript. This paper has received funding from the European Research Council (ERC) 