  For many problems, the important instances from practice possess certain
structure that one should reflect in the design of specific algorithms. As data
reduction is an important and inextricable part of today's computation, we
employ one of the most successful models of such precomputation -- the
kernelization. Within this framework, we focus on Traveling Salesperson Problem
(TSP) and some of its generalizations.
  We provide a kernel for TSP with size polynomial in either the feedback edge
set number or the size of a modulator to constant-sized components. For its
generalizations, we also consider other structural parameters such as the
vertex cover number and the size of a modulator to constant-sized paths. We
complement our results from the negative side by showing that the existence of
a polynomial-sized kernel with respect to the fractioning number, the combined
parameter maximum degree and treewidth, and, in the case of Subset-TSP,
modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely.
