A graph is planar if it can be drawn on flat paper so that no lines cross each other.
Suppose G is a component where every node has degree 2, and no node in G has arc to itself. Is G necessarily planar?
I tend to think that every graph is planar but I have no idea how to prove it. Any ideas?
I suppose it is enough to prove for components. Every connected graph which is 2-regular is a cycle. Since you are not considering loops, we leave out the cycle on one vertex (but you should note that a cycle on 1 vertex is still planar and the vertex has degree 2). Every cycle is planar. That is to say every 2-regular connected graph is planar.