Boundary classes of planar graphs

Authors:
Vadim Lozin
Affiliations:
Mathematics institute, university of warwick, coventry, cv4 7al, uk (e-mail: v.lozin@warwick.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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Abstract

We analyse classes of planar graphs with respect to various properties such as polynomial-time solvability of the dominating set problem or boundedness of the tree-width. A helpful tool to address this question is the notion of boundary classes. The main result of the paper is that for many important properties there are exactly two boundary classes of planar graphs.