Group edge choosability of planar graphs without adjacent short cycles

Abstract

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.