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The line-width of the optical transitions in quantum dots is studied theoretically on the basis of the electron coupling to the longitudinal optical phonons in polar semiconductors. With using the self-consistent Born approximation to the electronic self-energy, we are able to reproduce one of the main experimental results obtained on CdSe and CuBr quantum dots, namely the linear dependence of the width of the optical line on the inverse of the quantum dot diameter. In addition to it, the theory allows to expect certain resonance features on the linear dependence of line width. We remind that perhaps extensions of the present line-width theory might be suitable for to describe adequately the behavior of the line width in CdSe and InAs quantum dots.