A note on list edge and list total coloring of planar graphs without adjacent short cycles.

Let G be a planar graph with maximum degree Δ. In this paper, we prove that if any 4-cycle is not adjacent to an i-cycle for any i ∈ {3, 4} in G, then the list edge chromatic number xl′ ( G) = Δ and the list total chromatic number xl″ ( G) = Δ+1. [ABSTRACT FROM AUTHOR]