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标题：Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages
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作者：Michael A. Bekos ; Giordano Da Lozzo ; Svenja M. Griesbach 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：164
页码：16:1-16:17
DOI：10.4230/LIPIcs.SoCG.2020.16
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Book embeddings; Book thickness; Nonplanar graphs; Planar skeleton