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Twin-width is a newly introduced graph width parameter that aims atgeneralizing a wide range of "nicely structured" graph classes. In this work,we focus on obtaining good bounds on twin-width $\text{tww}(G)$ for graphs $G$from a number of classic graph classes. We prove the following:  - $\text{tww}(G) \leq 3\cdot 2^{\text{tw}(G)-1}$, where $\text{tw}(G)$ is thetreewidth of $G$,  - $\text{tww}(G) \leq \max(4\text{bw}(G),\frac{9}{2}\text{bw}(G)-3)$ for aplanar graph $G$ with $\text{bw}(G) \geq 2$, where $\text{bw}(G)$ is thebranchwidth of $G$,  - $\text{tww}(G) \leq 183$ for a planar graph $G$,  - the twin-width of a universal bipartite graph $(X,2^X,E)$ with $|X|=n$ is$n - \log_2(n) +  \mathcal{O}(1)$ .  An important idea behind the bounds for planar graphs is to use an embeddingof the graph and sphere-cut decompositions to obtain good bounds onneighbourhood complexity.

Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs