  A graph $G$ is $(a,b)$-choosable if for any color list of size $a$ associated
with each vertex, one can choose a subset of $b$ colors such that adjacent
vertices are colored with disjoint color sets. This paper proves that for any
integer $m\ge 1$, every finite triangle-free induced subgraph of the triangular
lattice is $(5m,2m)$-choosable.
