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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))

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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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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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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

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