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 computational problems on the …

[参考文献] Reinhard Diestel: Graph Theory (Fifth Edition) 本章的目标是一个定理：每个有限的图集合中，都存在两个图使得其中一个是另一个的子式。 图子式：如果无向图H可以通过图G删除 …

In this section, we explore the following process: 1) bounding the treewidth of a graph, 2) nding the corresponding tree decomposition for this bounded treewidth, and 3) using dynamic …

A graph with tree width w has a tree decomposition where every vertex is labeled by a set of size w+1; the reason for taking the size of the label set to be w+1 is to ensure that trees have tree …

Tree decompositions # This module implements tree-decomposition methods. A tree-decomposition of a graph G = (V, E) is a pair (X, T), where X = {X 1, X 2, …, X t} is a family of …

Let (T, W) be a tree-decomposition of a graph G, and let H be a complete subgraph of G. Prove that there exists t ∈ V (T ) such that V (H) ⊆ Wt. Deduce that the complete graph Kn has tree …

2011年1月21日 · A tree decomposition is a mapping of a graph into a related tree with desirable properties that allow it to be used to efficiently compute certain properties (e.g., independence …

A tree-decomposition of a graph G is a representation of G in a tree-like structure. From this structure it is possible to deduce certain connectivity properties of G.

We say that a graph G has an H-decomposition if there exists a set L of subgraphs of G, which are isomorphic to H, such that every edge of G appears in exactly one member of L. Note that …

2024年3月13日 · In graph theory, a decomposition tree is a decomposition of a graph into separators, connected in a tree. Proposed by Paul Seymour and Neil Robertson in their theory …