发表机构
Institute of Computing Science and Technology; Guangzhou University（计算科学与技术研究所; 广州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过Hamilton连通核引理和结构方法，证明了若干圈-轮Ramsey数，包括R(C_14,W_11)=27等，并给出临界染色的完整分类，所有证明均为组合证明。
AI 中文摘要
设$W_s=K_1+C_{s-1}$表示有$s$个顶点的轮图。我们给出结构证明$R(C_{14},W_{11})=27$和$R(C_{15},W_{11})=29$。结合Chen等人的定理（对$n\ge16$），这些等式给出对所有$n\ge14$有$R(C_n,W_{11})=2n-1$。这两个边界值包含在早前的综述公告中。我们还给出$R(C_8,W_7)=15$、$R(C_9,W_7)=17$和$R(C_8,W_9)=15$的结构证明。共同出发点是Hamilton连通核引理。对于十一顶点轮，顶点连通性和与局部圈相关的二部图的匹配数的界产生一个九阶顶点割。具有指定端点的路径然后排除两个剩余顶点集的所有可能阶数对。对于较小的轮，我们使用临界圈染色的结构和局部圈缩短论证。我们还给出$(C_8,C_6)$-和$(C_9,C_6)$-临界染色的完整结构分类，恢复先前报告的计数24和26。所有证明都是组合的，不使用穷举图枚举。
英文摘要
Let $W_s=K_1+C_{s-1}$ denote the wheel on $s$ vertices. We give structural proofs that $R(C_{14},W_{11})=27$ and $R(C_{15},W_{11})=29$. Together with the theorem of Chen et al. for $n\ge16$, these equalities give $R(C_n,W_{11})=2n-1$ for every $n\ge14$. The two boundary values were included in an earlier survey announcement. We also give structural proofs of $R(C_8,W_7)=15$, $R(C_9,W_7)=17$, and $R(C_8,W_9)=15$. The common starting point is a Hamilton-connected core lemma. For the eleven-vertex wheel, bounds on vertex connectivity and on the matching number of a bipartite graph associated with a local cycle yield a vertex cut of order nine. Paths with prescribed endpoints then rule out every possible pair of orders of the two remaining vertex sets. For the smaller wheels, we use the structure of critical cycle colorings and local cycle-shortening arguments. We also give complete structural classifications of the $(C_8,C_6)$- and $(C_9,C_6)$-critical colorings, recovering the previously reported counts 24 and 26. All proofs are combinatorial and use no exhaustive graph enumeration.
