Reed [J.~Comb.~Theory B, 1999] showed that graphs of maximum degree $Δ\geq 10^{14}$ without $Δ$-cliques are $(Δ-1)$-colorable. We design a one-pass semi-streaming algorithm for computing such a coloring. Additionally, we prove that any one-pass $(Δ-k)$-coloring algorithm for $0\leq k < (Δ+1)/2$ requires $Ω(n(k+1))$ space.

翻译：Reed [J.~Comb.~Theory B, 1999] 证明了最大度$Δ\geq 10^{14}$且不含$Δ$-团（$Δ$-cliques）的图是$(Δ-1)$-可着色的。我们设计了一种单遍半流式算法来计算此类着色。此外，我们证明了对于$0\leq k < (Δ+1)/2$，任何单遍$(Δ-k)$-着色算法都需要$Ω(n(k+1))$的空间。