We prove that for all $\varepsilon>0$, there exists a positive integer $n_0$ such that if $G$ is a graph on $n\geq n_0$ vertices with $δ(G)\geq\tfrac{1}{2}(1 + \varepsilon)n$, then $G$ satisfies the Total Coloring Conjecture, that is, $χ_T(G)\leq Δ(G)+2$.
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