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 $Δ$ and the minimum degree $δ$. We give algorithms with complexity $O(1.3158^{n-0.7~Δ(G)})$ and $O(1.32^{n-0.73~Δ(G)})$ that determines if $G$ is 3-colorable, when $δ(G)\geq 8$ and $δ(G)\geq 7$, respectively.

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