The list linear arboricity of planar graphs with 7-cycles containing at most two chords

摘要

A graph G is linear-k-choosable if for any edge assignment L={L(e):e∈E(G)} of k positive integers, there exists an edge-coloring φ of G such that each color class induces a linear forest and φ(e) ∈ L(e) for all e ∈ E(G). In this paper, we prove that if G is a planar graph such that every 7-cycle of G contains at most two chords, then G is linear ⌈Δ+12⌉-choosable if Δ(G) ≥ 6, and G is linear ⌈Δ2⌉-choosable if Δ(G) ≥ 11.