Total coloring graphs with large minimum degree

Abstract

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 $\hat{I}´(G)\ge \frac{1}{2}(1+\epsilon )n$, then $G$ satisfies the Total Coloring Conjecture, that is, $\ddot{I}{‡}_T(G)\le \hat{I}”(G)+2$.

arXiv admin note: text overlap with arXiv:2405.07382