Graphs of bounded twin-width are quasi-polynomially χ-bounded

02/15/2022

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by   Michał Pilipczuk, et al.

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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^4t+3ω. In other words, we prove that graph classes of bounded twin-width are quasi-polynomially χ-bounded. This provides a significant step towards resolving the question of Bonnet et al. [ICALP 2021] about whether they are polynomially χ-bounded.