On the list chromatic index of graphs of tree-width 3 and maximum degree at least 7

TL;DR

This paper investigates the list chromatic index of graphs with tree-width 3 and maximum degree at least 7, establishing new results on their edge-choosability.

Contribution

It proves that graphs of tree-width 3 with maximum degree at least 7 are $ ext{Δ}$-edge-choosable, including 3-trees.

Findings

3-trees are $ ext{Δ}$-edge-choosable

Graphs of tree-width 3 and max degree ≥7 are $ ext{Δ}$-edge-choosable

Extension of edge-choosability results to specific graph classes

Abstract

Among other results, it is shown that 3-trees are $\Delta$-edge-choosable and that graphs of tree-width 3 and maximum degree at least 7 are $\Delta$-edge-choosable.