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  • 1 University of Pannonia Department of Computer Science and Systems Technology Egyetem u. 10 8200 Veszprém Hungary
  • 2 University of Szeged Bolyai Institute Aradi vértanúk tere 1 6720 Szeged Hungary
  • 3 Zhengzhou University Department of Mathematics Zhengzhou, Henan 450052 China
  • 4 Hefei University of Technology School of Management Hefei 230009 China
  • 5 Monash University School of Mathematical Sciences Victoria 3800 Australia
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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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