  The field of kernelization studies polynomial-time preprocessing routines for
hard problems in the framework of parameterized complexity. Although a
framework for proving kernelization lower bounds has been discovered in 2008
and successfully applied multiple times over the last three years, establishing
kernelization complexity of many important problems remains open. In this paper
we show that, unless NP is a subset of coNP/poly and the polynomial hierarchy
collapses up to its third level, the following parameterized problems do not
admit a polynomial-time preprocessing algorithm that reduces the size of an
instance to polynomial in the parameter:
  - EDGE CLIQUE COVER, parameterized by the number of cliques,
  - DIRECTED EDGE/VERTEX MULTIWAY CUT, parameterized by the size of the cutset,
even in the case of two terminals,
  - EDGE/VERTEX MULTICUT, parameterized by the size of the cutset, and
  - k-WAY CUT, parameterized by the size of the cutset.
  The existence of a polynomial kernelization for EDGE CLIQUE COVER was a
seasoned veteran in open problem sessions. Furthermore, our results complement
very recent developments in designing parameterized algorithms for cut problems
by Marx and Razgon [STOC'11], Bousquet et al. [STOC'11], Kawarabayashi and
Thorup [FOCS'11] and Chitnis et al. [SODA'12].
