Group edge choosability of planar graphs without adjacent short cycles
  In this paper, we aim to introduce the group version of edge coloring and list edge coloring, and prove that all 2-degenerate graphs along with some planar graphs without adjacent short cycles is group $(\Delta(G)+1)$-edge-choosable while some planar graphs with large girth and maximum degree is group $\Delta(G)$-edge-choosable. 
Xin Zhang, Guizhen Liu
math.CO cs.DM