2023/04/24 by Sandra Albrechtsen, Albrechtsen, Sandra
Engineering · #05C40 #05C83 (Primary) #06A07 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Lignin and Wood Chemistry
paper · pdf · doi:10.48550/arxiv.2304.12078
openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way. We show that, for every k ∈ ℕ, every tree-decomposition of a graph G which efficiently distinguishes all its k-tangles can be refined to a tree-decomposition whose parts are either too small to be home to a k-tangle, or as small as possible while being home to a k-tangle.