Abstract
Let G be a planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ⩾ 4 . Then the list chromatic index χ l ′ ( G ) = Δ and the list total chromatic number χ l ″ ( G ) = Δ + 1 if ( Δ , k ) ∈ { ( 7 , 4 ) , ( 6 , 5 ) , ( 5 , 8 ) } . Furthermore, χ l ′ ( G ) = Δ if ( Δ , k ) ∈ { ( 4 , 14 ) } .
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