**Definition**: Trees and Forests

Let \(G(V,E,\gamma)\) be an undirected graph.

- \(G\) is called a
**forest**, if it contains only acyclic components. - \(G\) is called a
**tree**, if it has only one acyclic component.

| | | | | Contributors: *bookofproofs* | References: [570]

## 1.**Proposition**: Equivalent Definitions of Trees

## 2.**Lemma**: Lower Bound of Leaves in a Tree

## 3.**Definition**: Spanning Tree

## 4.**Definition**: Graph Decomposable Into \(k\) Trees

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[570] **Krumke Sven O., Noltemeier Hartmut**: “Graphentheoretische Konzepte und Algorithmen”, Teubner, 2005, Auflage 1

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