This paper presents the first polynomial-space exact algorithm
for TSP in graphs with degree at most~6.
We develop a set of branching rules to aid the analysis of the branching
algorithm, and
we use the measure-and-conquer method to effectively analyze our
branching algorithm,
and we obtain a running time of $O^*(2.7467^n)$,
still advantageous over other known polynomial-space algorithms
for the TSP in general graphs.