Nordhaus-Gaddum for Treewidth

We prove that for every graph $G$ with $n$ vertices, the treewidth of $G$ plus the treewidth of the complement of $G$ is at least $n-2$. This bound is tight

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

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.Comment: arXiv admin note: substantial text overlap with arXiv:1504.0212