Some star-critical connected Ramsey numbers

Sun, Xiaoqian; Zhang, Yanbo

doi:10.22108/toc.2026.144868.2264

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	Some star-critical connected Ramsey numbers
Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 02 اسفند 1404 اصل مقاله (504.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2026.144868.2264
نویسندگان
Xiaoqian Sun؛ Yanbo Zhang^*
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, China
چکیده
The star-critical connected Ramsey number $r_c^(G,H)$, introduced by Moun, Jakhar, and Budden (\textit{TOC}, 2025), is a more deeply studied variant of the connected Ramsey number. For paths versus complete graphs, they obtained the exact values of $r_c^(P_m,K_n)$ when $m=5$ and when $n=3$. For stars versus complete graphs, they determined the exact values of $r_c^(K_{1,m},K_n)$ when $m=3$ and when $n=3$. We complete the generalization of both cases by establishing the exact values of $r_c^(P_m,K_n)$ for $m\ge 6$ and $n\ge 4$, and $r_c^*(K_{1,m},K_n)$ for $m\ge 4$ and $n\ge 4$. The former result disproves a conjecture proposed by Moun et al. (\textit{TOC}, 2025).
کلیدواژه‌ها
Ramsey number؛ connected Ramsey number؛ star-critical Ramsey number

مراجع
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Some star-critical connected Ramsey numbers