Abstract: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 $k \in \mathbb{N}$, 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.
From: Sandra Albrechtsen [view email]
[v1]
Mon, 24 Apr 2023 13:22:46 UTC (32 KB)
[v2]
Tue, 5 May 2026 14:42:32 UTC (34 KB)
[v3]
Wed, 1 Jul 2026 05:31:25 UTC (34 KB)
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