%0 Journal Article
%T Minimal counterexamples and discharging method
%A Tao Wang
%J Computer Science
%D 2014
%I arXiv
%X 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 $\kappa$.
%U http://arxiv.org/abs/1403.0622v1