List injective coloring of planar graphs

An injective coloring is a vertex coloring (not necessarily proper) such that any two ver-tices sharing a common neighbor receive distinct colors. A graph G is called injectively k-choosable, if for any color list L with admissible colors on V(G) of size k , there is an injective coloring phi such that phi(v) is an element of L(v) whenever v is an element of V (G) . The list injective chromatic number, denoted by chi(l)(i) (G) , is the least k for which G is injectively k-choosable. We focus on the study of list injective coloring on planar graphs which has disjoint 5(-)-cycles and show that chi(l)(i) (G ) <= Delta + 3 if Delta >= 18 and chi(l)(i)(G ) <= Delta + 4 if Delta >= 12 .(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

An injective coloring is a type of vertex coloring where any two vertices sharing a common neighbor have different colors. The study of list injective coloring mainly focuses on planar graphs, and we have discovered that for graphs with a degree of at least 18, the minimum list injective chromatic number is less than or equal to the degree plus 3. Similarly, for graphs with a degree of at least 12, the minimum list injective chromatic number is less than or equal to the degree plus 4.