# Twin-width and permutations

arXiv: https://arxiv.org/abs/2102.06880 · HTML: https://mlsanity.com/paper/2102.06880/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [Component twin-width as a parameter for BINARY-CSP and its semiring generalisations](https://mlsanity.com/paper/2207.12368/) (2022)

## Abstract (arXiv)

Inspired by a width invariant on permutations defined by Guillemot and Marx, Bonnet, Kim, Thomass'e, and Watrigant introduced the twin-width of graphs, which is a parameter describing its structural complexity. This invariant has been further extended to binary structures, in several (basically equivalent) ways. We prove that a class of binary relational structures (that is: edge-colored partially directed graphs) has bounded twin-width if and only if it is a first-order transduction of a~proper permutation class. As a by-product, we show that every class with bounded twin-width contains at most 2O(n) pairwise non-isomorphic n-vertex graphs.