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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 edgeswhile ensuring that two edges that are adjacent receive different colors. Totalcoloring is the problem of coloring the edges and the vertices while ensuringthat two edges that are adjacent, two vertices that are adjacent, or a vertexand an edge that are incident receive different colors. In their listextensions, instead of having the same set of colors for the whole graph, everyvertex or edge is assigned some set of colors and has to be colored from it. Agraph 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 triangleadjacent to a $C_4$ are minimally edge and total choosable (Li Xu 2011), andthat planar graphs with $\Delta\geq 7$ and no triangle sharing a vertex with a$C_4$ or no triangle adjacent to a $C_k$ ($\forall 3 \leq k \leq 6$) areminimally total colorable (Wang Wu 2011). We strengthen here these results andprove that planar graphs with $\Delta\geq 7$ and no triangle adjacent to a$C_4$ are minimally edge and total choosable.

Planar graphs with $\Delta\geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable