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Let $G$ be an $n$-vertex graph with the maximum degree $\Delta$ and theminimum degree $\delta$. We give algorithms with complexity$O(1.3158^{n-0.7~\Delta(G)})$ and $O(1.32^{n-0.73~\Delta(G)})$ that determinesif $G$ is 3-colorable, when $\delta(G)\geq 8$ and $\delta(G)\geq 7$,respectively.

Improved algorithm to determine 3-colorability of graphs with the minimum degree at least 7