Maximum average degree of list-edge-critical graphs and Vizing's conjecture - Joshua Harrelson; Hannah Reavis (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2022)
Vizing conjectured that χ′ℓ(G)≤Δ + 1 for all graphs. For a graph G and nonnegative integer k, we say G is a k-list-edge-critical graph if χ′ℓ(G)>k, but χ′ℓ(G − e)≤k for all e ∈ E(G). We use known results for list-edge-critical graphs to verify Vizing’s conjecture for G with mad(G)<(Δ + 3)/2 and Δ ≤ 9.