For level-k phylogenetic networks, the paper proves treewidth is at most (k+3)/2, improves this to about k/3 for large k, and shows some level-k networks have treewidth at least k/13.
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Bounds on the Treewidth of Level-k Rooted Phylogenetic Networks
For level-k phylogenetic networks, the paper proves treewidth is at most (k+3)/2, improves this to about k/3 for large k, and shows some level-k networks have treewidth at least k/13.