   Chapter 10.1, Problem 54ES ### 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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# For what values of m and n does the complete bipartite graph on (m,n) vertices have (a) an Euler circuit? (b) a Hamiltonian circuit? Justify your answers.

To determine

(a)

For what values of m and n does the complete bipartite graph on (m,n) vertices have an Euler circuit? Justify your answers.

Explanation

Given information An Euler circuit.

Calculation:

Km,n has an Euler circuit if and only if both m and n are positive even integers.

JUSTIFICATION:A graph has Euler circuit if and only if it is connected and every vertex has an even degree

To determine

(b)

For what values of m and n does the complete bipartite graph on (m,n) vertices have a Hamiltonian circuit? Justify your answers.

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