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A Note on Graph Coloring Extensions and List-Colorings

A Note on Graph Coloring Extensions and List-Colorings

Let $G$ be a graph with maximum degree $\Delta \geq 3$ not equal to $K_{\Delta +1}$ and let $P$ be a subset of vertices with pairwise distance, $d(P)$, between them at least $8$. Let each vertex $x$ be assigned a list of colors of size $\Delta$ if $x\in V\setminus P$ …