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 Nov 5 comment Prove that if there are $vw ∈ E(G)$ such that $f(v) \neq f(w)$ then $G$ contains the graph $P_4$ as an induced subgraph This is all the proof? Nov 5 comment Prove that if $G$ is P4-free then any two vertices $u$ and $v$ are in the same connected component if and only if $f(u) = f(v)$ Thank you! but why the drawing is only f (u) and v? Nov 5 comment Prove that if $G$ is P4-free then any two vertices $u$ and $v$ are in the same connected component if and only if $f(u) = f(v)$ Draw the graph for this exercise, please Nov 4 comment Prove that if there are $vw ∈ E(G)$ such that $f(v) \neq f(w)$ then $G$ contains the graph $P_4$ as an induced subgraph Prove that if G is P4-free then any two vertices u and v are in the same connected component if and only if f(u)=f(v) Nov 2 comment Prove that if there are $vw ∈ E(G)$ such that $f(v) \neq f(w)$ then $G$ contains the graph $P_4$ as an induced subgraph an example , please Nov 2 comment Prove that if there are $vw ∈ E(G)$ such that $f(v) \neq f(w)$ then $G$ contains the graph $P_4$ as an induced subgraph Draw the graph for this exercise, please