Stable graphs of bounded twin-width

Abstract

We prove that every class of graphs $\mathcal{C}$ that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width. This generalizes analogous results for classes of bounded linear cliquewidth and of bounded cliquewidth. It also implies that monadically stable classes of bounded twin-widthare linearly $\chi$-bounded.

45 pages, 5 figures