  For planar graphs, we consider the problems of \emph{list edge coloring} and
\emph{list total coloring}. Edge coloring is the problem of coloring the edges
while ensuring that two edges that are adjacent receive different colors. Total
coloring is the problem of coloring the edges and the vertices while ensuring
that two edges that are adjacent, two vertices that are adjacent, or a vertex
and an edge that are incident receive different colors. In their list
extensions, instead of having the same set of colors for the whole graph, every
vertex or edge is assigned some set of colors and has to be colored from it. A
graph is minimally edge or total choosable if it is list edge
$\Delta$-colorable or list total $(\Delta+1)$-colorable, respectively, where
$\Delta$ is the maximum degree in the graph.
  It is already known that planar graphs with $\Delta\geq 8$ and no triangle
adjacent to a $C_4$ are minimally edge and total choosable (Li Xu 2011), and
that planar graphs with $\Delta\geq 7$ and no triangle sharing a vertex with a
$C_4$ or no triangle adjacent to a $C_k$ ($\forall 3 \leq k \leq 6$) are
minimally total colorable (Wang Wu 2011). We strengthen here these results and
prove that planar graphs with $\Delta\geq 7$ and no triangle adjacent to a
$C_4$ are minimally edge and total choosable.

Discrete Mathematics;Combinatorics