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

Let $G$ be an $n$-vertex graph with the maximum degree $Delta$ and the minimum 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 determines if $G$ is 3-colorable, when $delta(G)geq 8$ and $delta(G)geq 7$, respectively.