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On the Pagenumber of the Cube-Connected Cycles

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Abstract

In this manuscript, we treat the book embedding of the cube-connected cycles. The book embedding of graphs is one of the graph layout problems and has been studied widely. We show that the pagenumber of CCC(n), n ≥ 4, is three and that of CCC(3) is two. This result is optimal since CCC(n) can not be embedded into two pages for n ≥ 4.

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References

  1. Chartrand G., Lesniak L.: Graphs & Digraphs, 4 edn. Chapman & Hall/CRC, Boca Raton (2004)

    Google Scholar 

  2. Chung F.R.K., Leighton F.T., Rosenberg A.L.: Embedding graphs in books: a layout problem with application to VLSI design. SIAM J. Algebraic Discret. Methods 8, 33–58 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dujmović V., Wood D.R.: Stacks, queues and tracks: layouts of graph subdivisions. Discret. Math. Theor. Comput. Sci. 7, 155–202 (2005)

    Google Scholar 

  4. Hasunuma T.: Embedding iterated line digraphs in books. Networks 40(2), 51–62 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Konoe, M., Hagiwara, K. Tokura, N.: On the pagenumber of hypercubes and cube-connected cycles. IEICE Trans. J71-D(3), 490–500 (1988) (in Japanese)

  6. Muder D.J., Weaver M.L., West D.B.: Pagenumber of complete bipartite graphs. J. Graph Theory 12, 469–489 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Preparata F.P., Vuillemin J.: The cube-connected cycles: a versatile network for parallel computation. Commun. ACM 24(5), 300–309 (1981)

    Article  MathSciNet  Google Scholar 

  8. Tanaka Y., Shibata Y.: On the pagenumber of trivalent Cayley graphs. Discret. Appl. Math. 154, 1279–1292 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Yannakakis, M.: Four pages are necessary and sufficient for planar graphs. In: Proceedings of 18th ACM symposium on theory of computing, pp.104–108 (1986)

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Authors and Affiliations

  1. Information Science Center, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu, Fukuoka, 804-8550, Japan

    Yuuki Tanaka

  2. Department of Computer Science, Graduate School of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Yukio Shibata

Authors
  1. Yuuki Tanaka
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  2. Yukio Shibata
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Correspondence to Yuuki Tanaka.

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Tanaka, Y., Shibata, Y. On the Pagenumber of the Cube-Connected Cycles. Math.Comput.Sci. 3, 109–117 (2010). https://doi.org/10.1007/s11786-009-0012-y

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  • DOI: https://doi.org/10.1007/s11786-009-0012-y

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