Twin-width and permutations

02/13/2021
by   Édouard Bonnet, et al.
0

Inspired by a width invariant defined on permutations by Guillemot and Marx, the twin-width invariant has been recently introduced by Bonnet, Kim, Thomassé, and Watrigant. 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, it shows that every class with bounded twin-width contains at most 2^O(n) pairwise non-isomorphic n-vertex graphs.

READ FULL TEXT

page 1

page 3

page 5

page 7

page 13

page 15

research
08/06/2023

Factoring Pattern-Free Permutations into Separable ones

We show that for any permutation π there exists an integer k_π such that...
research
04/26/2022

Twin-width VII: groups

Twin-width is a recently introduced graph parameter with applications in...
research
02/25/2022

Twin-width and Transductions of Proper k-Mixed-Thin Graphs

The new graph parameter twin-width, recently introduced by Bonnet, Kim, ...
research
02/23/2022

Bounds on the Twin-Width of Product Graphs

Twin-width is a graph width parameter recently introduced by Bonnet, Kim...
research
05/08/2020

On The Relational Width of First-Order Expansions of Finitely Bounded Homogeneous Binary Cores with Bounded Strict Width

The relational width of a finite structure, if bounded, is always (1,1) ...
research
10/12/2021

A SAT Approach to Twin-Width

The graph invariant twin-width was recently introduced by Bonnet, Kim, T...
research
09/12/2019

Examples, counterexamples, and structure in bounded width algebras

We study bounded width algebras which are minimal in the sense that ever...

Please sign up or login with your details

Forgot password? Click here to reset