An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. For planar graphs, a fundamental result is due to Yannakakis, who proposed an algorithm to compute embeddings of planar graphs in books with four pages. Our main contribution is a technique that generalizes this result to a much wider family of nonplanar graphs, which is characterized by a biconnected skeleton of crossing-free edges whose faces have bounded degree. Notably, this family includes all 1-planar and all optimal 2-planar graphs as subgraphs. We prove that this family of graphs has bounded book thickness, and as a corollary, we obtain the first constant upper bound for the book thickness of optimal 2-planar graphs.

中文翻译：

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书 Embeddings of Nonplanar Graphs with Small Faces in几页

图在书中的嵌入，称为书嵌入，包括其顶点沿书脊的线性排序以及将其边分配给书页，以便同一页面上的两条边不会交叉. 图的书本厚度是其所有书本嵌入的最小页数。对于平面图，一个基本结果归功于 Yannakakis，他提出了一种算法来计算四页书籍中平面图的嵌入。我们的主要贡献是一种将这一结果推广到更广泛的非平面图族的技术，其特征是具有无交叉边的双连通骨架，其面具有有界度。值得注意的是，该族包括所有 1 平面图和所有最优 2 平面图作为子图。我们证明这组图有界书厚，