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Ramsey Numbers Involving an Odd Cycle and Large Complete Graphs in Three Colors

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Abstract

It is shown that the Ramsey number \(r(C_{2m+1},C_{2m+1},K_t)\) is between \(\Omega \Big (t^{1+\frac{2}{2m-1}}/(\log t)^{\frac{4}{2m-1}}\Big )\) and \(O\Big (t^{\big (1+\frac{1}{m}\big )^2}/(\log t)^{\frac{2m+1}{m^2}}\Big )\) for fixed m and large t.

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Acknowledgements

We are grateful to Professor Schiermeyer and reviewers for their valuable comments and suggestions which improve the presentations of the results greatly.

Funding

Supported in part by NSFC (11871377, 11901001, 11931002).

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Authors and Affiliations

  1. Center for Pure Mathematics, School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Meng Liu

  2. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Yusheng Li

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  1. Meng Liu
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  2. Yusheng Li
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Correspondence to Meng Liu.

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Liu, M., Li, Y. Ramsey Numbers Involving an Odd Cycle and Large Complete Graphs in Three Colors. Graphs and Combinatorics 38, 182 (2022). https://doi.org/10.1007/s00373-022-02577-w

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