Eulerian directed graphs of bounded carving width are well-quasi-ordered by strong immersion, with a meta-theorem extending to labeled vertices and edge orderings.
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A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
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Well-Quasi-Ordering Eulerian Digraphs: Bounded Carving Width
Eulerian directed graphs of bounded carving width are well-quasi-ordered by strong immersion, with a meta-theorem extending to labeled vertices and edge orderings.
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Finding irrelevant vertices in linear time on bounded-genus graphs
A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
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An Overview of Universal Obstructions for Graph Parameters
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.