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The Ramsey Number for a Linear Forest versus Two Identical Copies of Complete Graphs

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Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

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Abstract

Let H be a graph with the chromatic number h and the chromatic surplus s. A connected graph G of order n is called H-good if R(G,H) = (n − 1)(h − 1) + s. We show that P n is 2K m -good for n ≥ 3. Furthermore, we obtain the Ramsey number R(L,2K m ), where L is a linear forest. In addition, we also give the Ramsey number R(L,H m ) which is an extension for R(kP n ,H m ) proposed by Ali et al. [1], where H m is a cocktail party graph on 2m vertices.

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Authors and Affiliations

  1. Combinatorial and Applied Mathematics Research Group, Faculty of Mathematics and Natural Sciences (FMIPA), Tadulako University (UNTAD), Jalan Soekarno-Hatta Km. 8, Palu, 94118, Indonesia

    I W. Sudarsana & S. Musdalifah

  2. Computational Science Research Group, Faculty of Science, Institut Teknologi Telkom, Jl. Telekomunikasi no.1, Bandung, 40257, Indonesia

    Adiwijaya

Authors
  1. I W. Sudarsana
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  2. Adiwijaya
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  3. S. Musdalifah
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Editors and Affiliations

  1. University of Florida, CSE Building, Room 566, P.O. Box 116120, 32611-6120, Gainesville, Florida, USA

    My T. Thai

  2. Department of Computer and Information Science and Technology, University of Florida, P.O. Box, USA

    Sartaj Sahni

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Sudarsana, I.W., Adiwijaya, Musdalifah, S. (2010). The Ramsey Number for a Linear Forest versus Two Identical Copies of Complete Graphs. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_24

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  • DOI: https://doi.org/10.1007/978-3-642-14031-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

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