The structure of obstructions to treewidth and pathwidth

Authors:
Janka Chlebíková
Affiliations:
Department of Information Education, Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovak Republic
Venue:
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Year:
2002

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Abstract

It is known that the class of graphs with treewidth (resp. pathwidth) bounded by a constant w can be characterized by a finite obstruction set obs(TW(w)) (resp. obs(PW(w))). These obstruction sets are known for w ≤ 3 so far. In this paper we give a structural characterization of graphs from obs(TW(w)) (resp. obs(PW(w))) with a fixed number of vertices in terms of subgraphs of the complement. Our approach also essentially simplifies known characterization of graphs from obs(TW(w)) (resp. obs(PW(w))) with (w + 3) vertices. Also for any w ≥ 3 a graph from obs(TW(w))\obs(PW(w)) is constructed, that solves an open problem.