  We propose a preprocessing algorithm for the multiway cut problem that
establishes its polynomial kernelizability when the difference between the
parameter $k$ and the size of the smallest isolating cut is at most $log(k)$.
To the best of our knowledge, this is the first progress towards kernelization
of the multiway cut problem. We pose two open questions that, if answered
affirmatively, would imply, combined with the proposed result, unconditional
polynomial kernelizability of the multiway cut problem.
