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On Crossing Numbers of 5-Regular Graphs

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Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

The paper attempts to classify 5-regular graphs according to their crossing numbers and with given number of vertices. In particular, it is shown that there exist no 5-regular graphs on 12 vertices with crossing number one. This together with a result in [2] imply that the minimum number of vertices in a 5-regular graph with girth three and crossing number one is 14.

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References

  1. Chartrand, G., Lesniak, L.: Graphs & Digraphs. 3rd edn. Chapman & Hall, New York (1996)

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  2. Chia, G.L., Gan, C.S.: Minimal regular graphs with given girths and crossing numbers, (submitted)

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  3. Guy, R.K., Hill, A.: The crossing number of the complement of a circuit. Discrete Math. 5 (1973) 335–344

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  4. Kleitman, D.J.: The crossing number of K5, n. J. Combinat. Theory. 9 (1970) 315–323

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  5. McQuillan, D., Richter, R.B.: On 3-regular graphs having crossing number at least 2. J. Graph Theory. 18 (1994) 831–839

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  6. Richter, B.: Cubic graphs with crossing number two. J. Graph Theory. 12 (1988) 363–374

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    G. L. Chia

  2. Faculty of Engineering and Technology, Multimedia University, 75450, Malacca, Malaysia

    C. S. Gan

Authors
  1. G. L. Chia
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  2. C. S. Gan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Chia, G.L., Gan, C.S. (2002). On Crossing Numbers of 5-Regular Graphs. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_26

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  • DOI: https://doi.org/10.1007/3-540-45655-4_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

  • eBook Packages: Springer Book Archive

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