A note on total and list edge-colouring of graphs of tree-width 3

TL;DR

This paper proves new edge-choosability and total-colorability bounds for graphs with tree-width 3, including Halin graphs, advancing understanding of coloring properties in graph theory.

Contribution

It establishes that Halin graphs are Δ-edge-choosable and graphs of tree-width 3 are (Δ+1)-edge-choosable and (Δ+2)-total-colorable, providing new bounds for these classes.

Findings

Halin graphs are Δ-edge-choosable.

Graphs of tree-width 3 are (Δ+1)-edge-choosable.

Graphs of tree-width 3 are (Δ+2)-total-colorable.

Abstract

It is shown that Halin graphs are $\Delta$-edge-choosable and that graphs of tree-width 3 are $(\Delta+1)$-edge-choosable and $(\Delta +2)$-total-colourable.