Solution
= Solution
\b[True] for finite connected simple graphs. <average degree of a graph> at most two implies $e\leq v$. A <spanning tree> has $v-1$ edges, leaving at most one extra edge. Hence the graph is a <tree> or unicyclic. <trees> are planar, and a unicyclic graph is a cycle with <trees> attached to its vertices, which can also be embedded in the plane. Connectedness is essential to this argument: a disconnected nonplanar component can be diluted by isolated vertices.