A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. Let χi(G), χil(G) be the injective chromatic number and injective choosability number of G, respectively. Suppose that G is a planar graph with maximum degree Δ and girth g. We show that (1) if g≥5 then χil(G)≤Δ+7 for any Δ, and χil(G)≤Δ+4 if Δ≥13; (2) χil(G) ≤Δ+2 if g≥6 and Δ≥8; (3) χil(G)≤Δ+1 if g≥8 and Δ≥5. © © 2013 Elsevier B.V. All rights reserved.
Bu, Y., & Lu, K. (2013). List injective coloring of planar graphs with girth 5, 6, 8. Discrete Applied Mathematics, 161(10–11), 1367–1377. https://doi.org/10.1016/j.dam.2012.12.017