   Chapter 10.1, Problem 56ES ### 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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# Prove that if G is any bipartite graph, then every circuit in G has an even number of edges. Prove that if G is any graph with at least two vertices and if G does not have a circuit with an odd number of edges, then (G) is bipartite.

To determine

(a)

To prove:

If G is any bipartite graph, then every circuit in G has an even number of edges.

Explanation

Given information:

G is any bipartite graph.

Proof:

Given that G is bipartite.

Let X and Y are the two sets of vertices.

Since G is bipartite, every step alone a walk takes you either from X to Y or from Y to X...

To determine

(b)

To prove:

If G is any graph with at least two vertices and if G does not have a circuit with an odd number of edges, the G is bipartite.

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