Problem 3: For each of the two graphs below, determine whether they are planar. Justify your answer: if the graph is planar, show its planar embedding. If a graph is not planar, use Kuratowski's theorem to justify it. G h b H A h g b

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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### Problem 3: Planarity of Graphs G and H

#### Question:
For each of the two graphs below, determine whether they are planar. Justify your answer: if the graph is planar, show its planar embedding. If a graph is not planar, use Kuratowski's theorem to justify it.

##### Graph G:
Graph G consists of the following vertices:
- a
- b
- c
- d
- f
- g
- h

The edges are:
- (a, d), (a, c), (a, g)
- (c, d), (c, f), (c, b)
- (d, h)
- (f, b), (f, h)
- (g, b)

##### Graph H:
Graph H consists of the following vertices:
- a
- b
- c
- d
- f
- g
- h

The edges are:
- (a, d), (a, c), (a, g)
- (c, f), (c, g), (c, b)
- (d, h), (d, f)
- (f, h), (f, b)
- (g, b)

#### Analysis:
For both graphs, the problem is to determine their planarity and justify it using Kuratowski's theorem if necessary. 

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Transcribed Image Text:--- ### Problem 3: Planarity of Graphs G and H #### Question: For each of the two graphs below, determine whether they are planar. Justify your answer: if the graph is planar, show its planar embedding. If a graph is not planar, use Kuratowski's theorem to justify it. ##### Graph G: Graph G consists of the following vertices: - a - b - c - d - f - g - h The edges are: - (a, d), (a, c), (a, g) - (c, d), (c, f), (c, b) - (d, h) - (f, b), (f, h) - (g, b) ##### Graph H: Graph H consists of the following vertices: - a - b - c - d - f - g - h The edges are: - (a, d), (a, c), (a, g) - (c, f), (c, g), (c, b) - (d, h), (d, f) - (f, h), (f, b) - (g, b) #### Analysis: For both graphs, the problem is to determine their planarity and justify it using Kuratowski's theorem if necessary. ---
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