Abstract
In the current paper, we prove the 11-total choosability of planar graphs with maximum degree Δ ⩽ 8 , the ( Δ + 1 )-total choosability of 5-cycle-free planar graphs with maximum degree Δ ⩾ 8 , the 5-total choosability of graphs with maximum degree Δ = 4 and maximum average degree mad < 3 , and the 4-total choosability of subcubic graphs with maximum average degree mad < 9 4 .
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