INJECTIVELY DELTA CHOOSABLE GRAPHS

Title & Authors
INJECTIVELY DELTA CHOOSABLE GRAPHS
Kim, Seog-Jin; Park, Won-Jin;

Abstract
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. A graph G is said to be injectively $\small{k}$-choosable if any list $\small{L(v)}$ of size at least $\small{k}$ for every vertex $\small{v}$ allows an injective coloring $\small{{\phi}(v)}$ such that $\small{{\phi}(v){\in}L(v)}$ for every $\small{v{\in}V(G)}$. The least $\small{k}$ for which G is injectively $\small{k}$-choosable is the injective choosability number of G, denoted by $\small{{\chi}^l_i(G)}$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G) Keywords injective coloring;list coloring;maximum average degree;discharging; Language English Cited by References 1. O. V. Borodin and A. O. Ivanova, List injective colorings of planar graphs, Discrete Math. 311 (2011), no. 2-3, 154-165. 2. O. V. Borodin and A. O. Ivanova, 2-distance (${\Delta}+2$)-coloring of planar graphs with girth six and${\Delta}{\geq}18\$, Discrete Math. 309 (2009), no. 23-24, 6496-6502.

3.
Y. Bu, D. Chen, A. Raspaud, and W. Wang, Injective coloring of planar graphs, Discrete Appl. Math. 157 (2009), no. 4, 663-672.

4.
D. W. Cranston, S.-J. Kim, and G. Yu, Injective colorings of sparse graphs, Discrete Math. 310 (2010), no. 21, 2965-2973.

5.
A. Doyon, G. Hahn, and A. Raspaud, Some bounds on the injective chromatic number of graphs, Discrete Math. 310 (2010), 585-590.

6.
R. Li and B. Xu, Injective choosability of planar graphs of girth five and six, Discrete Math. 312 (2012), no. 6, 1260-1265.

7.
D. B. West, Introduction to Graph Theory, Prentice Hall Inc., Upper Saddle Rive, NJ, 2001.

8.
G. Wenger, Graphs with given diameter and a coloring problem, Technical Report, University of Dortmund, 1977.