  Nancy G. Kinnersley and Michael A. Langston has determined the excluded
minors for the class of graphs with path-width at most two by computer. Their
list consisted of 110 graphs. Such a long list is difficult to handle and gives
no insight to structural properties. We take a different route, and concentrate
on the building blocks and how they are glued together. In this way, we get a
characterization of 2-connected and 2-edge-connected graphs with path-width at
most two. Along similar lines, we sketch the complete characterization of
graphs with path-width at most two.
