We prove that any class of graphs with linear neighborhood complexity has bounded improper odd chromatic number. As a result, if $\mathcal{G}$ is the class of all circle graphs, or if $\mathcal{G}$ is any class with bounded twin-width, bounded merge-width, or a forbidden vertex-minor, then $\mathcal{G}$ is $χ_{\mathrm{o}}$-bounded.

翻译：我们证明了任何具有线性邻域复杂度的图类都具有有界非正常奇色数。因此，若$\mathcal{G}$为所有圆图构成的图类，或若$\mathcal{G}$为任意具有有界孪生宽度、有界合并宽度或存在禁止顶点子式的图类，则$\mathcal{G}$是$χ_{\mathrm{o}}$-有界的。