Missouri Journal of Mathematical Sciences

Graphs with Small Book Thickness

Shannon Overbay

Full-text: Open access

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.

Article information

Source
Missouri J. Math. Sci., Volume 19, Issue 2 (2007), 121-130.

Dates
First available in Project Euclid: 15 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1316092491

Digital Object Identifier
doi:10.35834/mjms/1316092491

Zentralblatt MATH identifier
1202.05029

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Citation

Overbay, Shannon. Graphs with Small Book Thickness. Missouri J. Math. Sci. 19 (2007), no. 2, 121--130. doi:10.35834/mjms/1316092491. https://projecteuclid.org/euclid.mjms/1316092491


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