Two smaller upper bounds of list injective chromatic number

Yuehua Bu (), Kai Lu and Sheng Yang
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Yuehua Bu: Zhejiang Normal University
Kai Lu: Zhejiang Normal University
Sheng Yang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 2, No 3, 373-388

Abstract: 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. Let $$\chi _{i}^{l}(G)$$ denote the list injective chromatic number of $$G$$ . We prove that (1) $$\chi _{i}^{l}(G)=\Delta $$ for a graph $$G$$ with the maximum average degree $$Mad(G)\le \frac{18}{7}$$ and maximum degree $$\Delta \ge 9$$ ; (2) $$\chi _{i}^{l}(G)\le \Delta +2$$ if $$G$$ is a plane graph with $$\Delta \ge 21$$ and without 3-, 4-, 8-cycles.

Keywords: Injective coloring; Maximum degree; Cycles; Maximum average degree (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9599-7

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