Two-Page Book Embeddings of 4-Planar Graphs

Authors Michael A. Bekos, Martin Gronemann, Chrysanthi N. Raftopoulou

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Michael A. Bekos
Martin Gronemann
Chrysanthi N. Raftopoulou

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Michael A. Bekos, Martin Gronemann, and Chrysanthi N. Raftopoulou. Two-Page Book Embeddings of 4-Planar Graphs. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 137-148, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


Back in the eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the class of 4-planar graphs. Our contribution consists of two algorithms: The first one is limited to triconnected graphs, but runs in linear time and uses existing methods for computing hamiltonian cycles in planar graphs. The second one, which solves the general case of the problem, is a quadratic-time algorithm based on the book embedding viewpoint of the problem.
  • Book Embedding
  • Subhamiltonicity
  • 4-Planar Graphs


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