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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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Bibliography (further reading)

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

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