Questions tagged [treewidth]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
0answers
42 views

Bounded treewidth implies bounded clique-width

We have a graph G of treewidth $\operatorname{tw}(G)\leq k$, for some $k\in\mathbb{N}$. I've seen a claim that that implies that the clique-width of the same graph is at most $k \cdot 2^k$. This ...
3
votes
2answers
177 views

Size of tree decomposition

Given a graph $G$ with $n$ vertices, let $(X, T)$ be a tree decomposition of $G$ with the smallest width. Is the number of nodes in $T$ upper bounded by $n$? I have googled it but all materials I ...
3
votes
3answers
56 views

treewidth of a given graph

Is the treewidth of this graph equal to 2? I have tried to prove it through the definition of a tree decomposition. If its not correct can someone give any hints?
5
votes
1answer
133 views

How does treewidth behave under graph minor operations?

It is a well-known fact that for any minor H of a graph G (commonly written as $H \leq_m G$), the treewidth of H is smaller than or equal to that of G. Minors of a graph are created through the ...