Context : Classical Wolf-Rayet ( WR ) stars are massive , hydrogen depleted , post main-sequence stars that exhibit emission-line dominated spectra .
For a given metallicity Z , stars exceeding a certain initial mass M ^ { WR } _ { single } ( Z ) can reach the WR phase through intrinsic mass-loss or eruptions ( single-star channel ) .
In principle , stars of lower masses can reach the WR phase via stripping through binary interactions ( binary channel ) .
Because winds become weaker at low Z , it is commonly assumed that the binary channel dominates the formation of WR stars in environments with low metallicity such as the Small and Large Magellanic Clouds ( SMC , LMC ) .
However , the reported WR binary fractions of 30 - 40 \% in the SMC ( Z = 0.002 ) and LMC ( Z = 0.006 ) are comparable to that of the Galaxy ( Z = 0.014 ) , and no evidence for the dominance of the binary channel at low Z could be identified observationally .
Here , we explain this apparent contradiction by considering the minimum initial mass M ^ { WR } _ { spec } ( Z ) needed for the stripped product to appear as a WR star .

Aims : By constraining M ^ { WR } _ { spec } ( Z ) and M ^ { WR } _ { single } ( Z ) , we estimate the importance of binaries in forming WR stars as a function of Z .

Methods : We calibrate M ^ { WR } _ { spec } ( Z ) using the lowest-luminosity WR stars in the Magellanic Clouds and the Galaxy .
A range of M ^ { WR } _ { single } values are explored using various evolution codes .
We estimate the additional contribution of the binary channel by considering the interval [ M ^ { WR } _ { spec } ( Z ) , M ^ { WR } _ { single } ( Z ) ] , which characterizes the initial-mass range in which the binary channel can form additional WR stars .

Results : The WR-phenomenon ceases below luminosities of \log L { \approx } 4.9 , 5.25 , and 5.6 [ L _ { \odot } ] in the Galaxy , the LMC , and the SMC , respectively , which translates to minimum He-star masses of 7.5 , 11 , 17 M _ { \odot } and minimum initial masses of M ^ { WR } _ { spec } = 18 , 23 , 37 M _ { \odot } .
Stripped stars with lower initial masses in the respective galaxies would tend to not appear as WR stars .
The minimum mass necessary for self-stripping , M ^ { WR } _ { single } ( Z ) , is strongly model dependent , but lies in the range 20 - 30 , 30 - 60 , and \gtrsim 40 M _ { \odot } for the Galaxy , LMC , and SMC , respectively .
We find that that the additional contribution of the binary channel is a non-trivial and model-dependent function of Z that can not be conclusively claimed to be monotonically increasing with decreasing Z .

Conclusions : The WR spectral appearance arises from the presence of strong winds .
Therefore , both M ^ { WR } _ { spec } and M ^ { WR } _ { single } increase with decreasing metallicity .
Considering this , we show that one should not a-priori expect that binary interactions become increasingly important in forming WR stars at low Z , or that the WR binary fraction grows with decreasing Z .