  The NP-hard graphical traveling salesman problem (GTSP) is to find a closed
walk of total minimum weight that visits each vertex in an undirected
edge-weighted and not necessarily complete graph. We present a problem kernel
with $\tau^2+\tau$ vertices for GTSP, where $\tau$ is the vertex cover number
of the input graph. Any $\alpha$-approximate solution for the problem kernel
also gives an $\alpha$-approximate solution for the original instance, for any
$\alpha\geq1$.
