Total coloring graphs with large minimum degree

We prove that for all $\epsilon >0$, there exists a positive integer $n_0$ such that if $G$ is a graph on $n\ge n_0$ vertices with $\delta (G)\ge \frac{1}{2}(1+\epsilon )n$, then $G$ satisfies the Total Coloring Conjecture, that is, ${\chi }_T(G)\le \mathrm{\Delta }(G)+2$.