In graph theory, a tree 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...

method, the hypertree decomposition, uses a different measure. Either way, the width of a decomposition is defined so that decompositions of size bounded by...

equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal...

bucket splits. The tree directory follows the spatial decomposition of the quadtree. A tree-pyramid (T-pyramid) is a "complete" tree; every node of the...

algorithm works on the tree decomposition. In general, a constraint satisfaction problem can be solved by first creating a tree decomposition and then using a...

path-decomposition is a tree decomposition (X,T) in which the underlying tree T of the decomposition is a path graph. The width of a path-decomposition is...

decomposition, decomposition of ideals into primary ideals Tree decomposition, homomorphism of a graph to a tree Vector decomposition, decomposition of vectors...

theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges...

property that is held by all cards). decomposition See tree decomposition, path decomposition, or branch-decomposition. degenerate degeneracy A k-degenerate...

theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of discrete mathematics at...

decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition,...

triplets pts = reshape(Img, [], 3); % Create OcTree decomposition object using a target bin capacity OT = OcTree(pts, 'BinCapacity', ceil((size(pts, 1) / 256)...

represented by the subtree of the tree decomposition descending from that bag. When G has bounded treewidth, it has a tree decomposition in which all bags have bounded...

as the decomposition of chordal graphs or strangulated graphs, no edges should be removed. In other contexts, such as the SPQR-tree decomposition of graphs...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

forms a tree decomposition of the graph, with treewidth equal to one less than the size of the largest clique in the graph; the tree decomposition of any...

graph. That is, a branch-decomposition may be viewed as a hierarchical clustering of the edges of the graph. Branch-decompositions and an associated numerical...

them. Decomposition relies on chemical processes similar to digestion in animals; in fact, many sources use the words digestion and decomposition interchangeably...

sequence is taken to be a cycle. An open ear decomposition or a proper ear decomposition is an ear decomposition in which the two endpoints of each ear after...

including directed rooted tree, out-arborescence, out-tree, and even branching being used to denote the same concept. Rooted tree itself has been defined...

separator hierarchy which may take the form of either a tree decomposition or a branch-decomposition of the graph. Separator hierarchies may be used to devise...

decomposition. Decomposition can be a gradual process for organisms that have extended periods of dormancy. One can differentiate abiotic decomposition from biotic...

easily derive a logarithmic upper bound on the tree-depth. The same technique, applied to a tree decomposition of a graph, shows that, if the treewidth of...

of decomposition techniques could be used in order to decrease the size of an equation set: decomposition-recombination planning algorithms, tree decomposition...

In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected...

structures underlying the SPQR tree, the triconnected components of a graph, and the connection between this decomposition and the planar embeddings of...

different use of 'tangle' appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, Journal of Combinatorial Theory...

a tree decomposition of an undirected graph, one less than the size of the largest vertex-set in the decomposition. Width of a path decomposition of...

into a tree-like structure called the split decomposition or join decomposition, which can be constructed in linear time. This decomposition has been...

of the graphs in H is planar, then every H-minor-free graph has a tree decomposition of bounded width; equivalently, it can be represented as a clique-sum...