Journal or Book Title
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 have distinct colors. A graph G is injectively k-choosable if for any list assignment L, where |L(v)| ≥ k for all v ∈ V(G), G has an injective L-coloring. Injective colorings have applications in the theory of error-correcting codes and are closely related to other notions of colorability. In this paper, we show that subcubic planar graphs with girth at least 6 are injectively 5-choosable. This strengthens the result of Lužar, Škrekovski, and Tancer that subcubic planar graphs with girth at least 7 are injectively 5-colorable. Our result also improves several other results in particular cases.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Brimkov, Boris; Edmond, Jennifer; Lazar, Robert; Lidicky, Bernard; Messerschmidt, Kacy; and Walker, Shanise, "Injective choosability of subcubic planar graphs with girth 6" (2017). Mathematics Publications. 122.
Available for download on Sunday, July 07, 2019