Four pages are indeed necessary for planar graphs

Authors

  • Michael Kaufmann Universität Tübingen
  • Michael Bekos Universität Tübingen
  • Fabian Klute Utrecht University
  • Sergey Pupyrev Facebook, Inc.
  • Chrysanthi Raftopoulou NTUA, Athens
  • Torsten Ueckerdt Karlsruhe Institute of Technology

DOI:

https://doi.org/10.20382/jocg.v11i1a12

Abstract

An embedding of a graph in a book consists of a linear order of its vertices along the spine of the book and of an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. Accordingly, the book thickness of a class of graphs is the maximum book thickness over all its members. In this paper, we address a long-standing open problem regarding the exact book thickness of the class of planar graphs, which previously was known to be either three or four. We settle this problem by constructing planar graphs that require four pages in all of their book embeddings, thus establishing that the book thickness of the class of planar graphs is four.

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Published

2020-08-10

Issue

Vol. 11 No. 1 (2020)

Section

Articles

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