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.
Barát, J., Width-type graph parameters, PhD thesis, University of Szeged, (2001), 90 pages.
Barát, J. and Hajnal, P., Operations which preserve path-width at most two, Comb. Probab. Comput., 10 (2001), 277–291. MR 1860436 (2002g: 05171)
Hajnal P., 'Operations which preserve path-width at most two' (2001) 10Comb. Probab. Comput.: 277-291.
Hajnal P.Operations which preserve path-width at most twoComb. Probab. Comput.200110277291)| false
Bodlaender, H. L. and de Fluiter, B., Intervalizing k-colored graphs, Technical report UU-CS-1995-15, 153 pages. MR 1466460. (English summary) Automata, languages and programming (Szeged, 1995), 87–98, Lecture Notes in Comput. Sci., 944, Springer, Berlin, 1995.
Bodlaender, H. L. and de Fluiter, B., On intervalizing k-colored graphs for DNA physical mapping, Discrete Appl. Math., 71 (1996), no. 1–3, 55–77. MR 1420292 (98d:92008)
Fluiter B., 'On intervalizing k-colored graphs for DNA physical mapping' (1996) 71Discrete Appl. Math.: 55-77.
Fluiter B.On intervalizing k-colored graphs for DNA physical mappingDiscrete Appl. Math.1996715577)| false
Diestel, R., Graph Minors I: a short proof of the path width theorem, Comb. Probab. Comput., 4 (1995), 27–30. MR 1336653 (96b:05077). Comment on: “Graph minors. I. Excluding a forest” [J. Combin. Theory Ser. B, 35 (1983), no. 1, 39–61; MR 0723569 (85d:05148)] by N. Robertson and P. D. Seymour (English summary).
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