  It is known that the problem of deleting at most k vertices to obtain a
proper interval graph (Proper Interval Vertex Deletion) is fixed parameter
tractable. However, whether the problem admits a polynomial kernel or not was
open. Here, we answers this question in affirmative by obtaining a polynomial
kernel for Proper Interval Vertex Deletion. This resolves an open question of
van Bevern, Komusiewicz, Moser, and Niedermeier.
