The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph $W_8$

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2024年6月26日

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Zhi Yee Chng,
Thomas Britz,
Ta Sheng Tan,
Kok Bin Wong

摘要

The Ramsey numbers $R(T_n,W_8)$ $R (T_{n}, W_{8})$ are determined for each tree graph $T_n$ $T_{n}$ of order $n\ge 7$ $n \geq 7$ and maximum degree $\Delta (T_n)$ $Δ (T_{n})$ equal to either $n-4$ $n - 4$ or $n-5$ $n - 5$ . These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that $R(T_n,W_m) = 2n-1$ $R (T_{n}, W_{m}) = 2 n - 1$ for each tree graph $T_n$ $T_{n}$ of order $n\ge m-1$ $n \geq m - 1$ with $\Delta (T_n)\le n-m+2$ $Δ (T_{n}) \leq n - m + 2$ when $m\ge 4$ $m \geq 4$ is even.

The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph \(W_8\)

摘要