Separation Number and Treewidth, Revisited

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Hussein Houdrouge , Babak Miraftab , Pat Morin This is my paper · ORCID

classification math.COcs.DM

keywords numberseparationtreewidthboundedconstructivefactfunctiongive

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abstract

We give a constructive proof of the fact that the treewidth of a graph $G$ is bounded by a linear function of the separation number of $G$.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Separation profiles of hyperbolic planar and apex-minor-free graphs
math.CO 2026-07 accept novelty 7.0 of 10

The separation profile of any δ-hyperbolic planar or apex-minor-free graph grows at most as C log n, answering Benjamini–Schramm–Timár affirmatively.
3-Colouring Planar Graphs
math.CO 2025-07 conditional novelty 7.0 of 10

Every n-vertex planar graph can be 3-coloured so that each monochromatic connected component has at most O(n^{4/9}) vertices, improving the previous O(n^{1/2}) bound.