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 ? l ? ( G ) ? Δ ( G ) + 2 if Δ ( G ) ? 6 , and ? l ' ( G ) = Δ ( G ) and ? l ? ( G ) = Δ ( G ) + 1 if Δ ( G ) ? 8 , where ? l ' ( G ) and ? l ? ( G ) denote the list edge chromatic number and list total chromatic number of G , respectively. Highlights? The list edge colorings and list total colorings of planar graphs without triangles adjacent 4-cycles are investigated. ? We proved that, if a planar graph G without triangles adjacent 4-cycles and Δ ( G ) ? 8 , then ? l ' ( G ) = Δ ( G ) . ? It is proved that ? l ? ( G ) ? Δ ( G ) + 2 , where G is a planar graph without triangles adjacent 4-cycles and Δ ( G ) ? 6 . ? It is proved that ? l ? ( G ) = Δ ( G ) + 1 , where G is a planar graph without triangles adjacent 4-cycles and Δ ( G ) ? 8 .