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At most single-bend embeddings of cubic graphs

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Abstract

This paper provides the complete proof of the fact that any planar cubic graph is at most single-bend embeddable except for the tetrahedron. AnO(n) amortized time algorithm for drawing an at most single-bend embedding of a cubic graph is also presented, wheren is the number of vertices of the graph. Furthermore, it is proved that the minimum of the total number of bends in an at most single-bend embedding of a cubic graph of ordern is less than or equal to 0.5n+1. This result is the best possible.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academia Sinica, 100080, Beijing

    Liu Yanpei, Marchioro P. & Petreschi R.

  2. Department of Mathematics, University of Rome “La Sapienza”, Rome, Italy

    Liu Yanpei, Marchioro P. & Petreschi R.

Authors
  1. Liu Yanpei
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  2. Marchioro P.
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  3. Petreschi R.
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Additional information

Supported by the Italian National Research Council and the first author was also supported by the National Natural Science Foundation of China

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Yanpei, L., Marchioro, P. & Petreschi, R. At most single-bend embeddings of cubic graphs. Appl. Math. 9, 127–142 (1994). https://doi.org/10.1007/BF02662066

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