the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is...

decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the...

coloring may be solved in polynomial time when the input is chordal. The treewidth of an arbitrary graph may be characterized by the size of the cliques...

graphs and the star height of regular languages. Intuitively, where the treewidth of a graph measures how far it is from being a tree, this parameter measures...

embedding, Hadwiger's conjecture, YΔY-reducible graphs, and relations between treewidth and graph diameter. Apex graphs are closed under the operation of taking...

second-order logic of graphs can be decided in linear time on graphs of bounded treewidth. The result was first proved by Bruno Courcelle in 1990 and independently...

And as with treewidth, many graph optimization problems may be solved efficiently for graphs of small branchwidth. However, unlike treewidth, the branchwidth...

It is NP-complete but fixed-parameter tractable on graphs of bounded treewidth. The monochromatic triangle problem takes as input an n-node undirected...

vertices in any of its bags; the treewidth of G is the minimum width of any tree decomposition of G. treewidth The treewidth of a graph G is the minimum width...

introduced by Seymour & Thomas (1993) as a tool for characterizing the treewidth of graphs. Their other applications include proving the existence of small...

The crucial property turns out to be treewidth, a measure of how tree-like the graph is. For a graph G of treewidth at most k and a graph H, the homomorphism...

structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be small for dense graphs. It is defined as the minimum...

per subgraph. Even stronger, for any fixed H, H-minor-free graphs have treewidth O ( n ) {\displaystyle \scriptstyle O({\sqrt {n}})} . The Hadwiger conjecture...

with each of the subgraphs. Brambles may be used to characterize the treewidth of G. A haven of order k in a graph G is a function β that maps each set...

searching number. Pathwidth and path-decompositions are closely analogous to treewidth and tree decompositions. They play a key role in the theory of graph minors:...

∞ Automorphisms 1 Chromatic number 0 Chromatic index 0 Genus 0 Properties Integral Symmetric Treewidth -1 Notation K0 Table of graphs and parameters...

bounded treewidth is necessary to allow exact, tractable inference, since the worst-case inference complexity is exponential in the treewidth k (under...

{\displaystyle k} -outerplanar graphs have treewidth at most 3 k − 1 {\displaystyle 3k-1} . However, some bounded-treewidth planar graphs such as the nested triangles...

the maximal graphs with a treewidth of k ("maximal" means that no more edges can be added without increasing their treewidth). They are also exactly the...

of graph, defined either as a subgraph of a k-tree or as a graph with treewidth at most k. Many NP-hard combinatorial problems on graphs are solvable...

whose treewidth is bounded by a constant can be performed in polynomial time. Here, the treewidth can be the primal treewidth, dual treewidth, or incidence...

a minor and also gave bounds for chordal graphs and graphs of bounded treewidth. The authors Foucaud et al. (2017a) proved bounds of the form n = O (...

D-separation Markov random field Tree decomposition (Junction tree) and treewidth Graph triangulation (see also Chordal graph) Perfect order Hidden Markov...

path problem is also fixed-parameter tractable when parameterized by the treewidth of the graph. For graphs of bounded clique-width, the longest path can...

Bodlaender, Hans L. (1998), "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1–2): 1–45, doi:10.1016/S0304-3975(97)00228-4...

is a 3-edge-connected graph. It is also a 3-tree, and therefore it has treewidth 3. Like any k-tree, it is a chordal graph. As a planar 3-tree, it forms...

computer science, It may be member of a series of graph parameters, see Treewidth § Hadwiger number and S-functions In physics, it may refer to: action...

Halin (1965), and is a precursor to the work of Robertson and Seymour linking treewidth to large grid minors, which became an important component of the algorithmic...

graphs can be recognized in linear time. Because Halin graphs have low treewidth, many computational problems that are hard on other kinds of planar graphs...

Halin graph is planar. Like outerplanar graphs, Halin graphs have low treewidth, making many algorithmic problems on them more easily solved than in unrestricted...