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Embedding Planar Graphs In Seven Pages

Lenwood S. Heath

Open publisher page 48 citations

Abstract

This paper investigates the problem of embedding planar graphs in books of few pages. An efficient algorithm for embedding a planar graph in a book establishes an upper bound of seven pages for any planar graph. This disproves a conjecture of Bernhart and Kainen that the pagenumber of a planar graph can be arbitrarily large. It is also shown that the stellations of K/sub 3/ have pagenumber three, the best possible.

About this research paper

What this paper is about

This paper investigates the problem of embedding planar graphs in books of few pages. An efficient algorithm for embedding a planar graph in a book establishes an upper bound of seven pages for any planar graph. This disproves a conjecture of Bernhart and Kainen that the pagenumber of a planar graph can be arbitrarily large. It is also shown that the stellations of K/sub 3/ have pagenumber three, the best possible.

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OpenAlex reports 48 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper investigates the problem of embedding planar graphs in books of few pages. An efficient algorithm for embedding a planar graph in a book establishes an upper bound of seven pages for any planar graph. This disproves a conjecture of Bernhart and Kainen that the pagenumber of a planar graph can be arbitrarily large. It is also shown that the stellations of K/sub 3/ have pagenumber three, the best possible.

Key concepts: Book embedding, Planar graph, Embedding, Planar straight-line graph, Planar, Outerplanar graph, Polyhedral graph, Conjecture

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