Graphs with chromatic number $(\chi(G) \ge 3 )$ other than odd cycle (Triangle free) Chromatic number denoted by $\chi(G)$ of graph $G$ is the minimum number of colours required to properly colour the given graph. 

For ODD Cycle chromatic number is 3 and it does not contain triangle as a subgraph. I thought about complete , star, wheel graphs etc, but they don't satisfy the conditions. 

I am looking for examples of graphs of $\chi(G)$ $\ge 3$, but does not contain a triangle or odd cycle as subgraph.
If a graph contains no odd cycle then it is bipartite and so 2-colorable.