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May 2007 Graphs with Small Book Thickness
Shannon Overbay
Missouri J. Math. Sci. 19(2): 121-130 (May 2007). DOI: 10.35834/mjms/1316092491

Abstract

In an article published in 1979, Kainen and Bernhart [1] laid the groundwork for further study of book embeddings of graphs. They define an $n$-book as a line $L$ in 3-space, called the spine, and $n$ half-planes, called pages, with $L$ as their common boundary. An $n$-book embedding of a graph $G$ is an embedding of $G$ in an $n$-book so that the vertices of $G$ lie on the spine and each edge of $G$ lies within a single page so that no two edges cross. The book thickness $bt(G)$ or page number $pg(G)$ of a graph $G$ is the smallest $n$ so that $G$ has an $n$-book embedding. Finding the book thickness of an arbitrary graph is a difficult problem. Even with a pre-specified vertex ordering, the problem has been shown to be NP-complete [6]. In this paper we will introduce book embeddings with particular focus on results for graphs with small book thickness.

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Shannon Overbay. "Graphs with Small Book Thickness." Missouri J. Math. Sci. 19 (2) 121 - 130, May 2007. https://doi.org/10.35834/mjms/1316092491

Information

Published: May 2007
First available in Project Euclid: 15 September 2011

zbMATH: 1202.05029
Digital Object Identifier: 10.35834/mjms/1316092491

Subjects:
Primary: 05C10

Rights: Copyright © 2007 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.19 • No. 2 • May 2007
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