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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

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Structure Theory for Tree Decompositions

I that $G=(V,E,W)$ is a weighted graph with positive edge weights and a finite set of vertices $K$. Let $0\le k,M\le K$ be a fixed integer. Is is known when $G$ admits the following type of decomposi …
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