Abstract
Given two non-empty graphs G, H and a positive integer k, the Gallai–Ramsey number \({\text {gr}}_k(G:H)\) is defined as the minimum integer N such that for all \(n\ge N\), every k-edge-coloring of \(K_n\) contains either a rainbow colored copy of G or a monochromatic copy of H. In this paper, we got some exact values or bounds for \({\text {gr}}_k(P_5:H) \ (k\ge 3)\) if H is a general graph or a star with extra independent edges or a pineapple.
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Acknowledgements
We would like to thank the anonymous referees for a number of helpful comments and suggestions.
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The authors have not disclosed any funding. This paper is supported by the National Science Foundation of China (Nos. 12061059, 11601254, 11551001) and the Qinghai Key Laboratory of Internet of Things Project (2017-ZJ-Y21).
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Zou, J., Wang, Z., Lai, HJ. et al. Gallai–Ramsey Numbers Involving a Rainbow 4-Path. Graphs and Combinatorics 39, 54 (2023). https://doi.org/10.1007/s00373-023-02648-6
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DOI: https://doi.org/10.1007/s00373-023-02648-6