The chromatic number of the following graph is _______.

The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .

let $$G$$ be a group with $$15$$ elements. Let $$L$$ be a subgroup of $$G$$. It is known that $$L \ne G$$ and that the size of $$L$$ is at least $$4$$. The size of $$L$$ is ______.

The maximum number of edges in a bipartite graph on $$12$$ vertices is _________.