Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

Publisher: PEARSON

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Chapter 13.1, Problem 20E

[BB] Prove that every planar graph V ≥ 2 vertices has at least two vertices of degree d ≤ 5 .
Prove that every planar graph with V ≥ 3 vertices has at least three vertices of degree d ≤ 5 .
Prove that every planar graph with V ≥ 4 vertices has at least four vertices of degree d ≤ 5 .

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Chapter 13.1, Problem 19E

Chapter 13.1, Problem 21E

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Chapter 13 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 13.1 - Prob. 1TFQ Ch. 13.1 - Prob. 2TFQ Ch. 13.1 - Prob. 3TFQ Ch. 13.1 - Prob. 4TFQ Ch. 13.1 - Prob. 5TFQ Ch. 13.1 - Prob. 6TFQ Ch. 13.1 - Prob. 7TFQ Ch. 13.1 - Prob. 8TFQ Ch. 13.1 - Prob. 9TFQ Ch. 13.1 - Prob. 10TFQ

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[BB] Prove that every planar graph V ≥ 2 vertices has at least two vertices of degree d ≤ 5 . Prove that every planar graph with V ≥ 3 vertices has at least three vertices of degree d ≤ 5 . Prove that every planar graph with V ≥ 4 vertices has at least four vertices of degree d ≤ 5 .

Solution Summary: The author proves that every planar graph with Vge 3 vertices and E edges has at least two degrees of dle 5.

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Chapter 13 Solutions