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# Forest and subgraph

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3.2 prove that a graph G is a forest if and only if every induced subgraph of G contains a vertex of degree at most 1.

Please can you explain in here when the graph G is a forest and induced subgraph.

https://brainmass.com/math/linear-algebra/forest-subgraph-98561

#### Solution Preview

A forest is a graph which has no cycles. The difference between a forest and a tree is that a tree is a connected graph with no cycles, while a forest may be disconnected; thus, every tree is a forest but not every forest is a tree.

An induced subgraph of a graph G is the subgraph obtained by taking some vertices in G and all of the edges between those vertices.

First we prove that if G is a forest, every induced ...

#### Solution Summary

This is an example of a proof regarding forest and subgraph.

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