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arXiv · 1510.05891

On the Book Thickness of 1-Planar Graphs

Md. Jawaherul Alam·Franz J. Brandenburg·Stephen G. Kobourov
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Abstract

In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called the pages of the book, such that two edges drawn on a page do not cross each other. The minimum number of pages in which a graph can be embedded is called the book-thickness or the page-number of the graph. It is known that every planar graph has a book embedding on at most four pages. Here we investigate the book-embeddings of 1-planar graphs. A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. We prove that every 1-planar graph has a book embedding on at most 16 pages and every 3-connected 1-planar graph has a book embedding on at most 12 pages. The drawings can be computed in linear time from any given 1-planar embedding of the graph.

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Md. Jawaherul Alam, Franz J. Brandenburg, Stephen G. Kobourov. 2015-10-20. On the Book Thickness of 1-Planar Graphs. https://arxiv.org/abs/1510.05891

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