Vizing's list edge coloring conjecture

Establish that every finite simple graph G with maximum degree Δ satisfies χ′_l(G) ≤ Δ + 1.

Background

The paper recalls Vizing's conjecture that the list edge chromatic number of every graph is at most one greater than its maximum degree. Although the conjecture is known for several graph classes, including graphs of maximum degree at most 4 and graphs of treewidth 3, it remains unresolved in general. The paper proves a signed analogue for signed graphs of treewidth 3 and for signed graphs of treewidth 4 with maximum degree at least 10, but does not settle the classical conjecture for all graphs.