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cs.DM — Discrete Mathematics

Fractional DAG treewidth controls DAG treewidth: profile reorientation and VC-dimension rounding

Contributed by Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník

For a nonempty finite graph, let $F$ be its fractional DAG treewidth, maximized over all acyclic orientations. Its DAG treewidth is at most $160F^3\ln(16F)$ . This answers the boundedness question of Bressan, Lanzinger, and Roth. Reorienting the graph converts shattered source profiles into projective-plane obstructions, which bound their VC dimension by $5F^2$ . Classical epsilon-net rounding then converts fractional bag covers to integral ones without changing the decomposition.

Primarily AI-generated textHuman understanding: some partsDAG treewidthVC dimensionepsilon netsfractional hypertreewidthgraph homomorphisms

Oct 15, 2026PDF ↗View work →

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Fractional DAG treewidth controls DAG treewidth: profile reorientation and VC-dimension rounding

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