We show that three subclasses of bounded treewidth graphs are well-quasi-ordered by refinements of the minor order. Specifically, we prove that graphs with bounded feedback-vertex-set are well-quasi-ordered by the topological-minor order, graphs with bounded vertex-covers are well-quasi-ordered by the subgraph order, and graphs with bounded circumference are well-quasi-ordered by the induced-minor order. Our results give an algorithm for recognizing any graph family in these classes which is closed under the corresponding minor order refinement. © 2009 Springer-Verlag.
CITATION STYLE
Fellows, M. R., Hermelin, D., & Rosamond, F. A. (2009). Well-quasi-orders in subclasses of bounded treewidth graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5917 LNCS, pp. 149–160). https://doi.org/10.1007/978-3-642-11269-0_12
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