Unavoidable Induced Subgraphs of Large 2-Connected Graphs

Ramsey proved that for every positive integer $n$, sufficiently large graph contains an induced $K_n$ or $\overline{K}_n$. Among the many extensions of Ramsey's Theorem there is analogue connected graphs: $K_n$, $K_{1,n}$, $P_n$. In this paper, we establish 2-connected graphs. particular, prove exceeding two, one following as subgraph: a subdivision $K_{2,n}$, $K_{2,n}$ with edge between two vertices degree and well-defined structure similar to ladder.