List injective coloring of a class of planar graphs without short cycles
Yuehua Bu, Chaoyuan Huang
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Source: Crossref
Published: Oct 1, 2018
DOI: 10.1142/s1793830918500684
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An injective [Formula: see text]-coloring of a graph [Formula: see text] is a mapping c: [Formula: see text]([Formula: see text]) [Formula: see text][Formula: see text] such that [Formula: see text] whenever [Formula: see text] have a common neighbor in [Formula: see text]. A list assignment of a graph [Formula: see text] is a mapping [Formula: see text] that assigns a color list [Formula: see text] to each vertex [Formula: see text]. Given a list assignment [Formula: see text] of [Formula: see text], an injective coloring [Formula: see text] of [Formula: see text] is called an injective [Formula: see text]-coloring if [Formula: see text] for every [Formula: see text]. In this paper, we show that if [Formula: see text] is a planar graph with girth [Formula: see text], then [Formula: see text] if [Formula: see text].
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