# Graphs with polynomially many minimal separators

@article{Abrishami2020GraphsWP, title={Graphs with polynomially many minimal separators}, author={Tara Abrishami and M. Chudnovsky and Cemil Dibek and St'ephan Thomass'e and Nicolas Trotignon and Kristina Vuvskovi'c}, journal={J. Comb. Theory, Ser. B}, year={2020}, volume={152}, pages={248-280} }

## 4 Citations

### Taming graphs with no large creatures and skinny ladders

- MathematicsESA
- 2022

We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class G there exists a constant k such that no member of G contains a k -creature as an induced…

### Disconnected Matchings

- MathematicsCOCOON
- 2021

This paper considers the generalized problem of finding c-disconnected matchings; such matchings are ones whose vertex sets induce subgraphs with at least c connected components and shows how to obtain a maximum connected matching in linear time given an arbitrary maximum matching in the input.

### Max Weight Independent Set in graphs with no long claws: An analog of the Gyárfás' path argument

- Mathematics, Computer ScienceICALP
- 2022

The Gyárfás’ path argument ensures that given an n -vertex P t -free graph, in polynomial time the authors can find a set P of at most t − 1 vertices, such that every connected component of G − N [ P ] has at most n/ 2 vertices.

### Dominated Minimal Separators are Tame (Nearly All Others are Feral)

- MathematicsArXiv
- 2020

A complete classification of all hereditary graph classes defined by a finite set of forbidden induced subgraphs into strongly quasi-tame or feral is obtained.

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