Group edge choosability of planar graphs without adjacent short cycles

TL;DR

This paper extends edge coloring concepts to group edge choosability, proving new bounds for planar graphs without adjacent short cycles and for graphs with large girth.

Contribution

It introduces the group edge coloring framework and establishes new choosability bounds for specific classes of planar graphs.

Findings

2-degenerate graphs are group (Δ(G)+1)-edge-choosable

Certain planar graphs without adjacent short cycles are group (Δ(G)+1)-edge-choosable

Planar graphs with large girth and high degree are group Δ(G)-edge-choosable

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.