On the Ramsey Numbers $R(S_{2,m}{K}_{2,q})$ and $R(s{K}_2,K_s+C_n)$

Abstract

We determine the Ramsey numbers $R(S_{2,m}{K}_{2,q})$ for $m\in \{3,4,5\}$ and $q\ge 2$. Additionally, we obtain $R(t{S}_{2,3},s{K}_{2,2})$ and $R(S_{2,3},s{K}_{2,2})$ for $s\ge 2$ and $t\ge 1$. Furthermore, we also establish $R(s{K}_2,\mathcal{H})$, where $\mathcal{H}$ is the union of graphs with each component isomorphic to the connected spanning subgraph of $K_s+C_n$, for $n\ge 3$ and $s\ge 1$.