Abstract
Let G be a planar graph with maximum degree Δ(G). In this paper, we prove that Gis (Δ(G)+1)-total choosable if G has no cycle of length from 4 to k and has minimum distance at least dΔ between triangles for (Δ(G),k,dΔ)=(6,4,1),(5,5,2),(5,6,1),(5,7,0),(4,6,3), (4,7,2),(4,10,1).
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