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Ramsey Numbers on a Union of Identical Stars Versus a Small Cycle

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Computational Geometry and Graph Theory (KyotoCGGT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4535))

Abstract

The Ramsey number for a graph G versus a graph H, denoted by R(G,H), is the smallest positive integer n such that for any graph F of order n, either F contains G as a subgraph or \(\overline F\) contains H as a subgraph. In this paper, we investigate the Ramsey numbers for stars versus small cycle. We show that R(S 8,C 4) = 10 and R(kS 1 + p ,C 4) = k(p + 1) + 1 for k ≥ 2 and p ≥ 3.

This research was supported by the ITB International Research Grants 2007 and 2008.

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References

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Author information

Authors and Affiliations

  1. Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Jalan Ganesa 10, Bandung, 40132, Indonesia

    Hasmawati, H. Assiyatun, E. T. Baskoro & A. N. M. Salman

Authors
  1. Hasmawati
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  2. H. Assiyatun
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  3. E. T. Baskoro
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  4. A. N. M. Salman
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Editor information

Editors and Affiliations

  1. School of Informatics, Kyoto University, Yosida-Honmati, 606-8501, Kyoto, Japan

    Hiro Ito

  2. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

  3. Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo-ku, 615-8540, Kyoto, Japan

    Naoki Katoh

  4. Graduate School of Science, Department of Mathematics and Information Sciences, Osaka Prefecture University, 599-8531, Sakai, Japan

    Yushi Uno

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© 2008 Springer-Verlag Berlin Heidelberg

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Hasmawati, Assiyatun, H., Baskoro, E.T., Salman, A.N.M. (2008). Ramsey Numbers on a Union of Identical Stars Versus a Small Cycle. In: Ito, H., Kano, M., Katoh, N., Uno, Y. (eds) Computational Geometry and Graph Theory. KyotoCGGT 2007. Lecture Notes in Computer Science, vol 4535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89550-3_9

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  • DOI: https://doi.org/10.1007/978-3-540-89550-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89549-7

  • Online ISBN: 978-3-540-89550-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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