On the structure of graphs with path-width at most two

Details On the structure of graphs with path-width at most two On the structure of graphs with path-width at most two

2009-10-26

arxiv.org/abs/0910.4889v1

Mathematics

Combinatorics

14 pages, 11 figures

Scientific paper

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.

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