List Edge Colorings of Planar Graphs without Non-induced 7-cycles

Abstract

A graph G is edge-k-choosable if, for any assignment of lists L(e)of at least k colors to all edges e ∈ E(G), there exists a proper edge coloring such that the color of e belongs to L(e) for all e ∈ E(G). One of Vizing’s classic conjectures asserts that every graph is edge-(Δ + 1)-choosable. It is known since 1999 that this conjecture is true for general graphs with Δ ≤ 4. More recently, in 2015, Bonamy confirmed the conjecture for planar graph with Δ ≥ 8, but the conjecture is still open for planar graphs with 5 ≤ Δ ≤ 7. We confirm the conjecture for planar graphs with Δ ≥ 6 in which every 7-cycle (if any) induces a C₇ (so, without chords), thereby extending a result due to Dong, Liu and Li.