Twin-width II: small classes

@inproceedings{Bonnet2020TwinwidthIS,
  title={Twin-width II: small classes},
  author={{\'E}douard Bonnet and Colin Geniet and Eun Jung Kim and St{\'e}phan Thomass{\'e} and R{\'e}mi Watrigant},
  booktitle={ACM-SIAM Symposium on Discrete Algorithms},
  year={2020}
}
The twin-width of a graph $G$ is the minimum integer $d$ such that $G$ has a $d$-contraction sequence, that is, a sequence of $|V(G)|-1$ iterated vertex identifications for which the overall maximum number of red edges incident to a single vertex is at most $d$, where a red edge appears between two sets of identified vertices if they are not homogeneous in $G$. We show that if a graph admits a $d$-contraction sequence, then it also has a linear-arity tree of $f(d)$-contractions, for some… 

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