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Context. Binary evolution can result in fast-rotating stars, predicted to beobservable as Be stars, through accretion of angular momentum duringmass-transfer phases. Despite numerous observational evidence pointing to thispossibly being the dominant Be formation channel, current models struggle toproduce a satisfactory description of Be star populations.  Aims. Given distinct uncertainties in detailed binary evolution calculations,we investigate a rigorous and model independent upper limit for the productionof Be stars through binary interaction and aim to confront this limit withobservations of Be stars in young star clusters.  Methods. Using extreme assumptions, we calculate the number ratio ofpost-interaction to pre-interaction binary systems in a coeval population,which describes an upper limit to Be star formation through mass-transfer. Adetailed comparison is made between our derived upper limit and relevantobservations of Be stars, which allows us to probe several aspects of binarystar physics.  Results. We find that in coeval populations, binary interaction can at mostaccount for one third of all main-sequence stars being Be stars. Near thecluster turn-off region, this limit appears to be realised in the clustersstudied. Away from the turn-off, applying simple assumptions about whichsystems undergo unstable mass-transfer produces a good fit to the observed Befraction as a function of mass.  Conclusions. We find that assuming distinct physics, binary evolution alonecan in principle match the high numbers of Be stars observed in open clusters.Whether the required binary physics is realised in nature remains to beinvestigated.

A stringent upper limit on Be star fractions produced by binary interaction