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- W3118992080 abstract "Chen et al. (Appl Math Lett 17:281–285, 2004) conjectured that for even m, $$R(T_n,W_m)=2n-1$$ if the maximum degree $$varDelta (T_n)$$ is small. However, they did not state how small it is. Related to this conjecture, it is also interesting to know which tree $$T_n$$ causes the Ramsey number $$R(T_n,W_m)$$ to be greater than $$2n-1$$ whenever m is even. In this paper, we determine the Ramsey number $$R(T_n,W_8)$$ for all trees $$T_n$$ with $$varDelta (T_n) ge n-3$$ . For most cases of these trees, $$R(T_n,W_8) > 2n-1$$ . Furthermore, we also prove that for certain values of n, the Ramsey number $$R(T_n,W_m)$$ is greater than $$2n-1$$ if $$varDelta (T_n) ge n-3$$ and m is even. Finally, we refine the above conjecture by giving an upper bound on the maximum degree of the tree $$T_n$$ ." @default.
- W3118992080 created "2021-01-18" @default.
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- W3118992080 date "2021-01-05" @default.
- W3118992080 modified "2023-09-27" @default.
- W3118992080 title "The Ramsey Number for Tree Versus Wheel with Odd Order" @default.
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- W3118992080 doi "https://doi.org/10.1007/s40840-020-01055-x" @default.
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