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INJECTIVELY DELTA CHOOSABLE GRAPHS
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 Title & Authors
INJECTIVELY DELTA CHOOSABLE GRAPHS
Kim, Seog-Jin; Park, Won-Jin;
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 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 -choosable if any list of size at least for every vertex allows an injective coloring such that for every . The least for which G is injectively -choosable is the injective choosability number of G, denoted by . In this paper, we obtain new sufficient conditions to be . Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < , then where and . In addition, when we prove that if mad(G) < , and when we prove that if mad(G) < . These results generalize some of previous results in [1, 4].
 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. crossref(new window)

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. crossref(new window)

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

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

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

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

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.