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arXiv · 2102.06880

Twin-width and permutations

Édouard Bonnet·Jaroslav Nešetřil·Patrice Ossona de Mendez·Sebastian Siebertz·Stéphan Thomassé
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Abstract

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 $2^{O(n)}$ pairwise non-isomorphic $n$-vertex graphs.

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Édouard Bonnet, Jaroslav Nešetřil, Patrice Ossona de Mendez, Sebastian Siebertz, Stéphan Thomassé. 2021-02-13. Twin-width and permutations. https://doi.org/10.46298/lmcs-20(3%3A4)2024

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