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Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 10.2 - Problem 50e
Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 10.2 - Problem 50e

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# Show that a graph is bipartite if, and only if, it does

ISBN: 9780495391326 48

## Solution for problem 50E Chapter 10.2

Discrete Mathematics with Applications | 4th Edition

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Problem 50E

Problem 50E

Show that a graph is bipartite if, and only if, it does not have a circuit with an odd number of edges. (See exercise for the definition of bipartite graph.)

bipartite graph

A bipartite graph G is a simple graph whose vertex set can be partitioned into two disjoint nonempty subsets V1 and V2 such that vertices in V1 may be connected to vertices in V2, but no vertices in V1 are connected to other vertices in V1 and no vertices in V2 are connected to other vertices in V2.For example, the graph G illustrated in (i) can be redrawn as shown in (ii). From the drawing in (ii), you can see that G is bipartite with mutually disjoint vertex sets V1 = {v1, v3, v5} and V2 = {v2, v4, v6}.

(i)

(ii)

Find which of the following graphs are bipartite. Redraw the bipartite graphs so that their bipartite nature is evident

a.

b.

c.

d.

e.

f.

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##### ISBN: 9780495391326

Since the solution to 50E from 10.2 chapter was answered, more than 749 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 50E from chapter: 10.2 was answered by , our top Math solution expert on 07/19/17, 06:34AM. The answer to “Show that a graph is bipartite if, and only if, it does not have a circuit with an odd number of edges. (See exercise for the definition of bipartite graph.)bipartite graphA bipartite graph G is a simple graph whose vertex set can be partitioned into two disjoint nonempty subsets V1 and V2 such that vertices in V1 may be connected to vertices in V2, but no vertices in V1 are connected to other vertices in V1 and no vertices in V2 are connected to other vertices in V2.For example, the graph G illustrated in (i) can be redrawn as shown in (ii). From the drawing in (ii), you can see that G is bipartite with mutually disjoint vertex sets V1 = {v1, v3, v5} and V2 = {v2, v4, v6}.(i) ________________(ii) Find which of the following graphs are bipartite. Redraw the bipartite graphs so that their bipartite nature is evidenta. ________________b. ________________c. ________________d. ________________e. ________________f.” is broken down into a number of easy to follow steps, and 155 words. This full solution covers the following key subjects: bipartite, vertices, graph, connected, other. This expansive textbook survival guide covers 131 chapters, and 5076 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics with Applications , edition: 4. Discrete Mathematics with Applications was written by and is associated to the ISBN: 9780495391326.

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