Consider the following statements:
- Any tree is $2$-colorable
- A graph $G$ has no cycles of even length if it is bipartite
- A graph $G$ is $2$-colorable if is bipartite
- A graph $G$ can be colored with $d+1$ colors if $d$ is the maximum degree of any vertex in the graph $G$
- A graph $G$ can be colored with $O(\log \mid v \mid )$ colors if it has $O(\mid v \mid )$ edges.
Choose the correct answer from the options given below:
- $(iii)$ and $(v)$ are incorrect
- $(ii)$ and $(iii)$ are incorrect
- $(ii)$ and $(v)$ are incorrect
- $(i)$ and $(iv)$ are incorrect