What is "treewidth"

n. (context mathematics computing English) The width (maximum number of nodes or leafs at any level) of a tree

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.

Treewidth is commonly used as a parameter in the parameterized complexity analysis of graph algorithms. The graphs with treewidth at most k are also called partial k-trees; many other well-studied graph families also have bounded treewidth.

The concept of treewidth was originally introduced by under the name of dimension. It was later rediscovered by , based on properties that it shares with a different graph parameter, the Hadwiger number. Later it was again rediscovered by and has since been studied by many other authors.