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A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2] A directed tree, [3] oriented tree, [4] [5] polytree, [6] or singly connected network [7] is a directed acyclic graph (DAG) whose underlying undirected graph is ...
Test whether adding the edge to the current forest would create a cycle. If not, add the edge to the forest, combining two trees into a single tree. At the termination of the algorithm, the forest forms a minimum spanning forest of the graph. If the graph is connected, the forest has a single component and forms a minimum spanning tree.
A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic. A polytree is an example of an oriented graph. The term polytree was coined in 1987 by Rebane and ...
The anarboricity of a graph is the maximum number of edge-disjoint nonacyclic subgraphs into which the edges of the graph can be partitioned. The star arboricity of a graph is the size of the minimum forest, each tree of which is a star (tree with at most one non-leaf node), into which the edges of the graph can be partitioned. If a tree is not ...
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests. An example of graphs with treewidth at most 2 are the series–parallel graphs.
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