  Recently, the author found that there is a common mistake in some papers by
using minimal counterexample and discharging method. We first discuss how the
mistake is generated, and give a method to fix the mistake. As an illustration,
we consider total coloring of planar or toroidal graphs, and show that: if $G$
is a planar or toroidal graph with maximum degree at most $\kappa - 1$, where
$\kappa \geq 11$, then the total chromatic number is at most $\kappa$.
