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
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
Section: Chapter Questions
Problem 1PE
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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.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa256fefa-da87-4b9d-ada9-af6adbfb8198%2F2d6ea169-f297-47c2-8e3b-eaebac411982%2Fd0nnlmq_processed.png&w=3840&q=75)
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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