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: Ang, Jorge L., Uy, Jeffrey L.
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Language:English
Published: Animo Repository 1995
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Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/16237
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Institution: De La Salle University
Language: English
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spelling oai:animorepository.dlsu.edu.ph:etd_bachelors-167502022-02-04T07:55:55Z On the coloring of empire maps Ang, Jorge L. Uy, Jeffrey L. 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. 1995-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/16237 Bachelor's Theses English Animo Repository Mappings (Mathematics) Graph theory Programming (Mathematics) Map-coloring problem
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Mappings (Mathematics)
Graph theory
Programming (Mathematics)
Map-coloring problem
spellingShingle Mappings (Mathematics)
Graph theory
Programming (Mathematics)
Map-coloring problem
Ang, Jorge L.
Uy, Jeffrey L.
On the coloring of empire maps
description 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.
format text
author Ang, Jorge L.
Uy, Jeffrey L.
author_facet Ang, Jorge L.
Uy, Jeffrey L.
author_sort Ang, Jorge L.
title On the coloring of empire maps
title_short On the coloring of empire maps
title_full On the coloring of empire maps
title_fullStr On the coloring of empire maps
title_full_unstemmed On the coloring of empire maps
title_sort on the coloring of empire maps
publisher Animo Repository
publishDate 1995
url https://animorepository.dlsu.edu.ph/etd_bachelors/16237
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