Mathematics in Computer Science

, Volume 3, Issue 1, pp 109–117 | Cite as

On the Pagenumber of the Cube-Connected Cycles

  • Yuuki TanakaEmail author
  • Yukio Shibata


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.


Cube-connected cycles Book embedding 

Mathematics Subject Classification (2000)



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  1. 1.
    Chartrand G., Lesniak L.: Graphs & Digraphs, 4 edn. Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  2. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 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. 4.
    Hasunuma T.: Embedding iterated line digraphs in books. Networks 40(2), 51–62 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 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)Google Scholar
  6. 6.
    Muder D.J., Weaver M.L., West D.B.: Pagenumber of complete bipartite graphs. J. Graph Theory 12, 469–489 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Preparata F.P., Vuillemin J.: The cube-connected cycles: a versatile network for parallel computation. Commun. ACM 24(5), 300–309 (1981)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Tanaka Y., Shibata Y.: On the pagenumber of trivalent Cayley graphs. Discret. Appl. Math. 154, 1279–1292 (2006)MathSciNetzbMATHGoogle Scholar
  9. 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)Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Information Science CenterKyushu Institute of TechnologyKitakyushuJapan
  2. 2.Department of Computer Science, Graduate School of EngineeringGunma UniversityKiryuJapan

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