Sufficient sparseness conditions for G2 to be (Δ+1)-choosable, when Δ≥5

Authors:
Daniel W. Cranston;Riste Škrekovski
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

We determine the list chromatic number of the square of a graph @g"@?(G^2) in terms of its maximum degree @D when its maximum average degree, denoted mad(G), is sufficiently small. For @D=6, if mad(G)=7+12@D-2, then @g"@?(G^2)=@D+1. Under the same conditions, @g"@?^i(G)=@D, where @g"@?^i is the list injective chromatic number.