Abstract
In this paper, we study the problem of testing whether a given graph admits a 2-page book embedding with a fixed edge partition. We first show that finding a 2-page book embedding of a given graph can be reduced to the planarity testing of a graph, which yields a simple linear-time algorithm for solving the problem. We then characterize the graphs that do not admit 2-page book embeddings via forbidden subgraphs, and give a linear-time algorithm for detecting the forbidden subgraph of a given graph.
This is an extended abstract. For the full version of this paper with omitted proofs, see [7].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Angelini, P., Di Bartolomeo, M., Di Battista, G.: Implementing a partitioned 2-page book embedding testing algorithm. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 79–89. Springer, Heidelberg (2013)
Angelini, P., Di Battista, G., Frati, F., Patrignani, M., Rutter, I.: Testing the simultaneous embeddability of two graphs whose intersection is a biconnected or a connected graph. J. Discrete Algorithms 14, 150–172 (2012)
Bernhart, F., Kainen, P.C.: The book thickness of a graph. J. Combin. Theory Ser. B 27(3), 320–331 (1979)
Biedl, T.: Drawing planar partitions III: Two constrained embedding problems, Technical Report RRR 12-98, RUTCOR, Rutgers University (1998)
Di Battista, G., Tamassia, R.: On-line maintenance of triconnected components with SPQR-trees. Algorithmica 15, 302–318 (1996)
Hong, S., Nagamochi, H.: Two-page book embedding and clustered graph planarity, TR[2009-004], Dept. of Applied Mathematics and Physics, University of Kyoto (2009)
Hong, S., Nagamochi, H.: Simpler testing for two page book embedding of partitioned graphs, TR[2013-001], Dept. of Applied Mathematics and Physics, University of Kyoto (2013)
Wigderson, A.: The complexity of the Hamiltonian circuit problem for maximal planar graphs, Technical Report 298, EECS Department, Princeton University (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Hong, SH., Nagamochi, H. (2014). Simpler Algorithms for Testing Two-Page Book Embedding of Partitioned Graphs. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-08783-2_41
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08782-5
Online ISBN: 978-3-319-08783-2
eBook Packages: Computer ScienceComputer Science (R0)