In a reduction sequence of a graph, vertices are successively identified until the graph has
one vertex. At each step, when identifying $ u $ and $ v $, each edge incident to exactly one …

We prove that every class of graphs that is monadically stable and has bounded twin-width
can be transduced from some class with bounded sparse twin-width. This generalizes …

Bonnet et al. J. ACM, 69 (2022), 3 introduced the twin-width of a graph. We show that the
twin-width of an n-vertex graph is less than (n+n\lnn+n+2\lnn)/2, and the twin-width of an m …

For every fixed $ d\in\mathbb {N} $, we design a data structure that represents a binary $
n\times n $ matrix that is $ d $-twin-ordered. The data structure occupies $ O_d (n) $ bits …

Bonnet et al.(FOCS 2020) introduced the graph invariant twin-width and showed that many
NP-hard problems are tractable for graphs of bounded twin-width, generalizing similar …

We prove that for every t∈ N there is a constant γ t such that every graph with twin-width at
most t and clique number ω has chromatic number bounded by 2 γ t log 4 t+ 3⁡ ω. In other …

The graph width-measure twin-width recently attracted great attention because of its solving
power and generality. Many prominent NP-hard problems are tractable on graphs of …

The modular decomposition of a graph G is a natural construction to capture key features of
G in terms of a labeled tree (T, t) whose vertices are labeled as “series”(1),“parallel”(0) or …

Twin-width is a width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant
[FOCS'20, JACM'22], which has many structural and algorithmic applications. We prove that …

The disjoint paths logic, FOL+ DP, is an extension of First-Order Logic (FOL) with the extra
atomic predicate dp k (x 1, y 1,…, xk, yk), expressing the existence of internally vertex …