Independent Set

You are given a graph $G$ with $N$ vertices (numbered $1$ through $N$) and $M$ edges. You should partition the vertices of $G$ into two sets $A$ and $B$ such that: - each vertex of $G$ belongs to exactly one of these sets - $A$ is non-empty - $A$ is an independent set in $G$, i.e. for each pair of vertices $u, v \in A$, $G$ does not contain an edge $(u, v)$ - for each vertex $a \in A$ and each