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.