Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.
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Hajnal P.Operations which preserve path-width at most twoComb. Probab. Comput.200110277291)| false
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Murty U. S. R.Graduate Texts in Mathematics2008)| false
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Fluiter B.On intervalizing k-colored graphs for DNA physical mappingDiscrete Appl. Math.1996715577)| false
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Diestel R., 'Graph Minors I: a short proof of the path width theorem' (1995) 4Comb. Probab. Comput.: 27-30.
Diestel R.Graph Minors I: a short proof of the path width theoremComb. Probab. Comput.199542730)| false