Talk:Book embedding

Arc diagrams


In See also Arc diagrams are referred to as two-page book embeddings. In Arc diagram it is discussed how some planar graphs can only be represented as topological two-page book embeddings. I propose this be expanded upon in this article.

67.252.103.23 (talk) 15:42, 11 June 2014 (UTC)
 * Yes, I'm working on expanding this article and intend to add a section here within the next few days on graph visualization applications of book embeddings. But note that the image you link above is *not* a book embedding, because one of its edges crosses from one page to another. —David Eppstein (talk) 15:48, 11 June 2014 (UTC)


 * I included it as an example of a topological book embedding, which is the section that I proposed needed expansion/disambiguation. 67.252.103.23 (talk) — Preceding undated comment added 16:32, 11 June 2014 (UTC)

Question: minor-closed families
I am confused by this statement:


 * "All minor-closed graph families, and in particular the graphs with bounded treewidth or bounded genus, also have bounded book thickness."

Consider the set of all graphs. As far as I understood the linked article and also this article, this set is minor-closed. But because this set also contains all complete graphs, it has an unbounded book thickness.

Am I making a mistake somewhere?

Does this sentence only apply to all other minor-closed graph families? If so, I propose to mention this.

Baum42 (talk) 11:02, 12 June 2015 (UTC)
 * Yes, all nontrivial minor-closed graph families. That one is an exception to most statements about minor-closed families. —David Eppstein (talk) 17:32, 12 June 2015 (UTC)

Blankenship–Oporowski conjecture disproven
I'm not adding this to this article or to List of unsolved problems in mathematics, at least not until it's been properly peer-reviewed and published, but https://arxiv.org/abs/2011.04195 provides a counterexample to the Blankenship–Oporowski conjecture. —David Eppstein (talk) 02:40, 10 November 2020 (UTC)