On the coloring of empire maps
To achieve a general solution to the problem of map coloring, empire maps are considered. Since previous studies on map coloring only made use of the four-color theorem, the results discussed in this paper also serve to generalize this famous theorem.Empire maps are defined as maps having sets of di...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1995
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16237 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | To achieve a general solution to the problem of map coloring, empire maps are considered. Since previous studies on map coloring only made use of the four-color theorem, the results discussed in this paper also serve to generalize this famous theorem.Empire maps are defined as maps having sets of different empires, where each empire can consist of several regions. Moreover, M-pire maps are empire maps in which each empire is composed of at most M regions.To solve the problem of empire map coloring, the notion of an M-pire graph is introduced and well-known results from graph theory are used.The general solution proven by Heawood, and which was further justified by Jackson and Ringel, is discussed in detail. A computer program illustrating the algorithm for empire map coloring based on the theorem of Heawood is also presented. |
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