If $G$ be a graph of order $6,$ then $G$ contains $C_3$ or $O_3$ as induced subgraph.
May I know if my proof is correct?
Suppose not. Let $v \in G.$ Consider the graph $H$ that is obtained by deleting $v$ and all edges incident to it. Since $H$ does not contain $C_3$ or $O_3, H = C_5.$ Now, if $v$ is adjacent to at least 3 vertices in $H,$ then we have a $C_3$ induced subgraph. If not, we have a $O_3$ induced subgraph formed by $v$ and any two non-adjacent vertices (that are not adjacent to $v$).
Thank you.