文摘
An injective coloring of a graph \(G\) is an assignment of colors to the vertices of \(G\) so that any two vertices with a common neighbor receive distinct colors. Let \(\chi _{i}^{l}(G)\) denote the list injective chromatic number of \(G\) . We prove that (1) \(\chi _{i}^{l}(G)=\Delta \) for a graph \(G\) with the maximum average degree \(Mad(G)\le \frac{18}{7}\) and maximum degree \(\Delta \ge 9\) ; (2) \(\chi _{i}^{l}(G)\le \Delta +2\) if \(G\) is a plane graph with \(\Delta \ge 21\) and without 3-, 4-, 8-cycles.