# The Book Thickness of 1-Planar Graphs is Constant

The Book Thickness of 1-Planar Graphs is Constant 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 $$O(\sqrt{n})$$ O ( n ) , where n is the number of vertices of the graph. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

# The Book Thickness of 1-Planar Graphs is Constant

, Volume 79 (2) – Aug 25, 2016
22 pages

/lp/springer_journal/the-book-thickness-of-1-planar-graphs-is-constant-fkFQbtfm0C
Publisher
Springer US
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0203-2
Publisher site
See Article on Publisher Site

### 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 $$O(\sqrt{n})$$ O ( n ) , where n is the number of vertices of the graph.

### Journal

AlgorithmicaSpringer Journals

Published: Aug 25, 2016

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