Edge choosability and total choosability of planar graphs with no 3-cycles adjacent 4-cycles

Two cycles are said to be adjacent if they share a common edge. Let G be a planar graph without triangles adjacent 4-cycles. We prove that χ l ″ ( G ) ≤ Δ ( G ) + 2 if Δ ( G ) ≥ 6 , and χ l ′ ( G ) = Δ ( G ) and χ l ″ ( G ) = Δ ( G ) + 1 if Δ ( G ) ≥ 8 , where χ l ′ ( G ) and χ l ″ ( G ) denote the list edge chromatic number and list total chromatic number of G , respectively.