Well-Quasi-Orders in Subclasses of Bounded Treewidth Graphs
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.
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