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arXiv · 1503.04990

The Book Thickness of 1-Planar Graphs is Constant

Michael A. Bekos·Till Bruckdorfer·Michael Kaufmann·Chrysanthi N. Raftopoulou
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Abstract

In a book embedding, the vertices of a graph are placed on the spine of a book and the edges are assigned to pages, so that edges on the same page do not cross. In this paper, we prove that every $1$-planar graph (that is, a graph that can be drawn on the plane such that no edge is crossed more than once) admits an embedding in a book with constant number of pages. To the best of our knowledge, the best non-trivial previous upper-bound is $O(\sqrt{n})$, where $n$ is the number of vertices of the graph.

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Michael A. Bekos, Till Bruckdorfer, Michael Kaufmann, Chrysanthi N. Raftopoulou. 2015-03-17. The Book Thickness of 1-Planar Graphs is Constant. https://arxiv.org/abs/1503.04990

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