Stable graphs of bounded twin-width
Jakub Gajarsk\'y, Micha{\l} Pilipczuk, Szymon Toru\'nczyk
TL;DR
This paper establishes a connection between monadically stable graph classes with bounded twin-width and classes with bounded sparse twin-width, extending previous results and showing linear chi-boundedness.
Contribution
It proves that monadically stable classes with bounded twin-width can be transduced from classes with bounded sparse twin-width, generalizing prior results for bounded linear cliquewidth.
Findings
Monadically stable classes with bounded twin-width can be transduced from classes with bounded sparse twin-width.
Such classes are linearly chi-bounded.
Generalizes results for classes with bounded linear cliquewidth and bounded cliquewidth.
Abstract
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 analogous results for classes of bounded linear cliquewidth and of bounded cliquewidth. It also implies that monadically stable classes of bounded twin-widthare linearly -bounded.
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Taxonomy
TopicsAdvanced Graph Theory Research · Finite Group Theory Research · Nuclear Receptors and Signaling