Jakub Gajarsk'y, Michal Pilipczuk, Szymon Toruńczyk
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引用次数: 23
摘要
我们证明了每一类单根稳定且双宽有界的图都可以由一类稀疏双宽有界的图转化而来。这推广了有界线性cliquewidth类[Nešetřil et al. 2021b]和有界cliquewidth类[Nešetřil et al. 2021a]的类似结果。它还表明有界双宽度的单根稳定类是线性χ-有界的。
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 [Nešetřil et al. 2021b] and of bounded cliquewidth [Nešetřil et al. 2021a]. It also implies that monadically stable classes of bounded twin-width are linearly χ-bounded.
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