Treewidth

A graph with eight vertices, and a tree decomposition of it onto a tree with six nodes. Each graph edge connects two vertices that are listed together at some tree node, and each graph vertex is listed at the nodes of a contiguous subtree of the tree. Each tree node lists at most three vertices, so the width of this decomposition is two.

The four forbidden minors for treewidth 3: K5 (top-left), the graph of the octahedron (bottom-left), the Wagner graph (top-right), and the graph of the pentagonal prism (bottom-right)

In graph theory, the treewidth of an undirected graph is a number associated with the graph. Treewidth may be defined in several equivalent ways: from the size of the largest vertex set in a tree decomposition of the graph, from the size of the largest clique in a chordal completion of the graph, from the maximum order of a haven describing a strategy for a pursuit-evasion game on the graph, or from the maximum order of a bramble, a collection of connected subgraphs that all touch each other.

单词	Treewidth
释义	Treewidth 英语百科 Treewidth In graph theory, the treewidth of an undirected graph is a number associated with the graph. Treewidth may be defined in several equivalent ways: from the size of the largest vertex set in a tree decomposition of the graph, from the size of the largest clique in a chordal completion of the graph, from the maximum order of a haven describing a strategy for a pursuit-evasion game on the graph, or from the maximum order of a bramble, a collection of connected subgraphs that all touch each other.
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