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 κ−1, where
κ≥11, then the total chromatic number is at most κ.Comment: 8 pages. Preliminary version, comments are welcom