   Chapter 10.6, Problem 20ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Suppose G is a connected graph and T is a circuitfree subgraph of G. Suppose also that if any edge e of G not in T is added to T, the resulting graph contains a circuit. Prove that T is a spanning tree for G.

To determine

The proof of the given statement about spanning tree.

Explanation

Given information:

A proposition is given as,

Suppose G is a connected graph and T is a circuit free subgraph of G. Suppose also that if any edge e of G not in T is added to T, the resulting graph contains a circuit. Prove that T is a spanning tree for G.

Calculation:

There can be two cases for the given subgraph T either it is connected, or it is disconnected.

Case 1(Connected):

According to the given information the given subgraph is circuit free and we have assumed that it is connected so all vertices are reachable

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