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On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices

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 For given two graphs G dan H, the Ramsey number R(G,H) is the smallest positive integer n such that every graph F of order n must contain G or the complement of F must contain H. In [12], the Ramsey numbers for the combination between a star S n and a wheel W m for m=4,5 were shown, namely, R(S n ,W 4)=2n−1 for odd n and n≥3, otherwise R(S n ,W 4)=2n+1, and R(S n ,W 5)=3n−2 for n≥3. In this paper, we shall study the Ramsey number R(G,W m ) for G any tree T n . We show that if T n is not a star then the Ramsey number R(T n ,W 4)=2n−1 for n≥4 and R(T n ,W 5)=3n−2 for n≥3. We also list some open problems.

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Received: October, 2001 Final version received: July 11, 2002

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ID="*" This work was supported by the QUE Project, Department of Mathematics ITB Indonesia

Acknowledgments. We would like to thank the referees for several helpful comments.

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Baskoro , E., Surahmat, ., Nababan, S. et al. On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices. Graphs Comb 18, 717–721 (2002). https://doi.org/10.1007/s003730200056

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  • DOI: https://doi.org/10.1007/s003730200056

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