Questions tagged [treewidth]

Questions regarding the treewidth of graphs. Graphs of low treewidth admit fast divide-and-conquer algorithms for many graph problems that are NP-hard on general graphs.

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Complexity of the homomorphism problem parameterized by treewidth

The homomorphism problem $\text{Hom}(\mathcal{G}, \mathcal{H})$ for two classes $\mathcal{G}$ and $\mathcal{H}$ of graphs is defined as follows: Input: a graph $G$ in $\mathcal{G}$, a graph $H$ in $...
14
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0answers
166 views

Counting solutions to extended MSO formulas, and sampling — do these appear in the literature?

I am trying to determine if the literature contains various extensions of Courcelle's theorem. Since I haven't been able to find these in the literature, I guess that these are folklore results, or ...
7
votes
0answers
86 views

Complexity of computing the simplicial width of a graph

Let $G=(V,E)$ be a finite undirected graph. A tree decomposition $(T,\lambda)$ of $G$ is a tree $T$ with labeling function $\lambda : T \to 2^{V}$ such that: For every edge $\{v_1,v_2\} \in E$, there ...
6
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0answers
126 views

Grid-Minor Theorem of Robertson and Seymour and its Algorithmic Applications

Graph-Minor Theorem of Robertson and Seymour [1] states that if graph G has large treewidth, then it contains a large grid as minor. Most approximation results on general classes of graphs with ...
6
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0answers
104 views

Deterministic approximation algorithms for treewidth

As far as I understand, the factor $O(\sqrt{\log OPT})$ approximation algorithm for treewidth of Feige, Hajiaghayi, and Lee is randomized, and no deterministic approximation algorithm with this factor ...
6
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0answers
208 views

Decomposition based on approximate separators in graph

Suppose I want to find vertex subset $S$ of graph $G=(V,E)$ such that any simple closed walk that visits vertices both in $S$ and in $V\backslash S$ has length $\ge g$ The idea is to relax ...
5
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0answers
123 views

How much does treewidth changes after removal of a path?

Let $G$ be a graph such that $\mathrm{tw}(G)=t$. Let $t' = \min\limits_{u,v \in V(G)} \max\limits_{P \text{ is a path from } u \text{ to } v} \mathrm{tw}(G - P)$. Then how small $t'$ can be? My ...
4
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0answers
333 views

How to go from a DAG model to bounded treewidth?

I am cross posting this question from CS.SE since I believe it is research-related question. Given a Bayesian Network DAG $G$, we can transform it into a junction tree $T_G$ by performing two steps:...
4
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0answers
110 views

Approximating Front Size of Asymmetric Matrices

The front size of a matrix $A$ is the largest number of non-zeros below the diagonal in any column of its Cholesky factor. If $A$ is symmetric then the minimum front size of $A$ is equal to the ...
2
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0answers
135 views

Paper regarding the complexity of the longest path problem on weighted directed graphs of bounded treewidth

I would like to cite a paper/report/etc that solves the following problem polynomially in $n$: Given a weighted directed graph $G=(V,E)$, $|V|=n$, of bounded treewidth $k \in \mathbb{N}$ and a source-...
2
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0answers
448 views

Tree decomposition for DAGs

Tree decompositions and treewidth are a standard way to measure how close an undirected graph is to a tree. I am studying decompositions of directed acyclic graphs (DAGs), and have come to define them ...
1
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88 views

Directed NP Hard Problem on DAG

There are problems that are NP-Hard on undirected graphs(maximum weight independent set and graph coloring) but are polynomial time solvable on trees. Tree decomposition is a good tool to talk about ...