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Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5] Monochromatic triangle [3]: GT6 Pathwidth, [6] or, equivalently, interval thickness, and vertex separation number [7] Rank coloring; k-Chinese postman
Two different tree-decompositions of the same graph. The width of a tree decomposition is the size of its largest set X i minus one. The treewidth tw(G) of a graph G is the minimum width among all possible tree decompositions of G. In this definition, the size of the largest set is diminished by one in order to make the treewidth of a tree ...
A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v, then the label of u is smaller than the label of v). In a rooted tree, the parent of a vertex v is the vertex connected to v on the path to the root; every vertex has a unique parent, except the root has no parent. [24]
The left tree is the decision tree we obtain from using information gain to split the nodes and the right tree is what we obtain from using the phi function to split the nodes. The resulting tree from using information gain to split the nodes. Now assume the classification results from both trees are given using a confusion matrix.
A cutpoint, cut vertex, or articulation point of a graph G is a vertex that is shared by two or more blocks. The structure of the blocks and cutpoints of a connected graph can be described by a tree called the block-cut tree or BC-tree. This tree has a vertex for each block and for each articulation point of the given graph.
In any split graph, one of the following three possibilities must be true: [10] There exists a vertex x in i such that C ∪ {x} is complete. In this case, C ∪ {x} is a maximum clique and i is a maximum independent set. There exists a vertex x in C such that i ∪ {x} is independent.
A cut or split is trivial when one of its two sides has only one vertex in it; every trivial cut is a split. A graph is said to be prime (with respect to splits) if it has no nontrivial splits. [2] Two splits are said to cross if each side of one split has a non-empty intersection with each side of the other split.
See decision tree. As compared to regression analysis, which creates a formula that health care providers can use to calculate the probability that a patient has a disease, recursive partition creates a rule such as 'If a patient has finding x, y, or z they probably have disease q'. A variation is 'Cox linear recursive partitioning'. [2]