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- W3022158524 abstract "Given graphs G and H and a positive integer k, the Gallai–Ramsey number, denoted by $$gr_{k}(G : H)$$ is defined to be the minimum integer n such that every coloring of $$K_{n}$$ using at most k colors will contain either a rainbow copy of G or a monochromatic copy of H. We consider this question in the cases where $$G in {P_{4}, P_{5}}$$. In the case where $$G = P_{4}$$, we completely solve the Gallai–Ramsey question by reducing to the 2-color Ramsey numbers. In the case where $$G = P_{5}$$, we conjecture that the problem reduces to the 3-color Ramsey numbers and provide several results in support of this conjecture." @default.
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- W3022158524 date "2020-05-02" @default.
- W3022158524 modified "2023-09-25" @default.
- W3022158524 title "Gallai–Ramsey Numbers for Rainbow Paths" @default.
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- W3022158524 doi "https://doi.org/10.1007/s00373-020-02175-8" @default.
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