Criticality of a graph What's the usual method for proving the criticality of a graph? I've been trying out different methods and theorems but I can't find a decent method that's really convincing. Thanks a lot in advance!

If $G$ is $n$-critical (i.e. $\chi(G) = n$), then $\delta(G) \geq n-1$. So if $\delta(G) < n-1$ then $G$ is not $n$-critical.