Spanning Tree - Spanning Forests

Spanning Forests

A spanning forest is a type of subgraph that generalises the concept of a spanning tree. However, there are two definitions in common use. One is that a spanning forest is a subgraph that consists of a spanning tree in each connected component of a graph. (Equivalently, it is a maximal cycle-free subgraph.) This definition is common in computer science and optimization. It is also the definition used when discussing minimum spanning forests, the generalization to disconnected graphs of minimum spanning trees. Another definition, common in graph theory, is that a spanning forest is any subgraph that is both a forest (contains no cycles) and spanning (includes every vertex).

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Famous quotes containing the word forests:

    The great pines stand at a considerable distance from each other. Each tree grows alone, murmurs alone, thinks alone. They do not intrude upon each other. The Navajos are not much in the habit of giving or of asking help. Their language is not a communicative one, and they never attempt an interchange of personality in speech. Over their forests there is the same inexorable reserve. Each tree has its exalted power to bear.
    Willa Cather (1873–1947)