For every δ < 3/2 the ⊆-minimal minor-closed classes with density >δ form a finite explicitly identified set, yielding a 2^poly(n)-time algorithm that computes δ(excl(Z)) or reports ≥3/2 for any finite forbidden-minor set Z.
Seymour , title =
5 Pith papers cite this work. Polarity classification is still indexing.
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Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
Proves the Dallard et al. conjecture holds for outerstring graphs and sharpens bounds on tree-independence number for multiple K_{1,d}-free classes.
The paper establishes treewidth bounds and MSO-axiomatizability results for weak memory models, introduces reads-from robustness, and derives algorithmic implications for verification.
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
citing papers explorer
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Obstructions for Minor-Closed Classes of limiting Densities Below 3/2
For every δ < 3/2 the ⊆-minimal minor-closed classes with density >δ form a finite explicitly identified set, yielding a 2^poly(n)-time algorithm that computes δ(excl(Z)) or reports ≥3/2 for any finite forbidden-minor set Z.
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Counting Small Induced Subgraphs: Hardness of Symmetry-Based Properties
Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
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Tree-independence number of $K_{1,d}$-free graph classes
Proves the Dallard et al. conjecture holds for outerstring graphs and sharpens bounds on tree-independence number for multiple K_{1,d}-free classes.
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An MSO Framework for Weak-Memory Verification and Robustness
The paper establishes treewidth bounds and MSO-axiomatizability results for weak memory models, introduces reads-from robustness, and derives algorithmic implications for verification.