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Operations Which Preserve Path-Width at Most Two

Published online by Cambridge University Press:  02 October 2001

JÁNOS BARÁT  and
PÉTER HAJNAL
JÁNOS BARÁT
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720 Hungary (e-mail: jbarat@math.u-szeged.hu, hajnal@math.u-szeged.hu)
PÉTER HAJNAL
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720 Hungary (e-mail: jbarat@math.u-szeged.hu, hajnal@math.u-szeged.hu)
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Abstract

The number of excluded minors for the class of graphs with path-width at most two is very large. To give a practical characterization of the obstructions, we introduce some operations which preserve path-width at most two. We give a list of ten graphs such that any graph with path-width more than two can be reduced – by taking minors and applying our operations – to one of the graphs on our list. We think that our operations and excluded substructures give a far more transparent description of the class of graphs with path-width at most two than Kinnersley and Langston's characterization by 110 excluded minors (see [4]).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 4 , July 2001 , pp. 277 - 291
Copyright
2001 Cambridge University Press

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