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Planar graphs
Author
Toh, Wee Teck
Supervisor
Dong, F. M., 1962-
Abstract
In this Academic Exercise, we are concerned with a special class of graphs, known as "planar graphs". It is one of the fundamental concepts in Graph Theory. Due to its wide practical applications, Graph Theorists have long been interested in studying in great detail about the planar graphs, i.e., their criterion and their properties.
The main objectives of this Academic Exercise are as follows:
1. to present the proof of a necessary and sufficient condition for planar graphs, i.e., Kuratowski's Theorem,
2. to present the proof of a similar necessary and sufficient condition for outerplanar graphs,
3. to present the proof of the 5-Colour Theorem, and
4. to present the proof of some equivalences of the 4-Colour Theorem,
In the process, we shall also briefly discuss the following:
1. the properties of planar graphs,
2. the properties of outerplanar graphs,
3. the history and implications of the 4-Colour Theorem, and
4. the outline of Tait's and Kempe's "proofs" of the 4-Colour Theorem, along with the mistakes that they committed.
The main objectives of this Academic Exercise are as follows:
1. to present the proof of a necessary and sufficient condition for planar graphs, i.e., Kuratowski's Theorem,
2. to present the proof of a similar necessary and sufficient condition for outerplanar graphs,
3. to present the proof of the 5-Colour Theorem, and
4. to present the proof of some equivalences of the 4-Colour Theorem,
In the process, we shall also briefly discuss the following:
1. the properties of planar graphs,
2. the properties of outerplanar graphs,
3. the history and implications of the 4-Colour Theorem, and
4. the outline of Tait's and Kempe's "proofs" of the 4-Colour Theorem, along with the mistakes that they committed.
Date Issued
2004
Call Number
QA166 Toh
Date Submitted
2004