Ramsey \((K_{1,2},C_{4})\)-Minimal Graphs

For any given graphs \( G \) and \( H \), we write \( F \rightarrow (G, H) \) to mean that any red-blue coloring of the edges of \( F \) contains a red copy of \( G \) or a blue copy of \( H \). A graph \( F \) is \((G, H)\)-minimal (Ramsey-minimal) if \( F \rightarrow (G, H) \) but \( F^* \not\rightarrow (G, H) \) for any proper subgraph \( F^* \subset F \). The class of all \((G, H)\)-minimal graphs is denoted by \( \mathcal{R}(G, H) \). In this paper, we will determine the graphs in \( \mathcal{R}(K_{1,2}, C_4) \).