Lately I read an old paper by Paul Erdős and L. Pósa ("On the maximal number of disjoint circuits of a graph") and stumbled across the following step in a proof (I changed it a bit to be easier to read):
It is well known and easy to show that every (undirected) graph with $n < 10$ vertices, where all vertices have a degree $\geq 3$ contains a circuit of at most $4$ edges.
I would be very happy if someone could enlighten me how this is simple and why he can conclude that, maybe there are some famous formulas for graphs that make this trivial? For the ones interested, he also mentions that a counterexample for $n=10$ is the petersen graph.