Identifying the two colouring pattern

Many graph problems may look completely unrelated at first, but can be reduced to the two-colouring problem. These are generally medium problems where we need to find if a graph is two-colourable or not. Since bipartite graphs are equivalent to two-colourable graphs, checking a graph for being bipartite is the same as checking it for two-colourability. In some cases, we may need to make some critical observations to reduce the problem to the two-colouring problem and prove that the solution to the two-colouring problem also solves the original problem. 

If the problem statement or its solution follows the generic template below, it can be solved using the two-colouring technique.