List edge chromatic number of graphs with large girth (Q1197027)

The list edge chromatic number \(le\chi(G)\) of a graph \(G\) is the smallest integer \(k\) such that whenever each edge \(e\in E(G)\) is assigned a list \(\varphi(e)\) of \(k\) admissible colors, then there exists a proper coloring \(f\) of \(E(G)\) so that each \(e\in E(G)\) is colored by a color \(f(e)\in\varphi(e)\). It is shown that if \(G\) has maximum degree \(\Delta\) and girth at least \(8\Delta(ln\Delta+1.1)\), then \(le\chi(G)=\Delta\) or \(\Delta+1\).