Every triangle-free induced subgraph of the triangular lattice is   $(5m,2m)$-choosable
  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. 
Yves Aubry (IML, IMATH), Jean-Christophe Godin (IMATH), Olivier Togni   (Le2i)
math.CO