A Original Solution To The 4 Colours Theorem | OMICS International | Abstract
ISSN: 1736-4337

# Journal of Generalized Lie Theory and ApplicationsOpen Access

OMICS International organises 3000+ Global Conferenceseries Events every year across USA, Europe & Asia with support from 1000 more scientific Societies and Publishes 700+ Open Access Journals which contains over 50000 eminent personalities, reputed scientists as editorial board members.

Open Access Journals gaining more Readers and Citations

This Readership is 10 times more when compared to other Subscription Journals (Source: Google Analytics)

## A Original Solution To The 4 Colours Theorem

Degree in Mathematics, UNED University, Spain

*Corresponding Author:
Degree in Mathematics
UNED University, Spain
Tel:
91 398 60 00
E-mail: [email protected]

Received date: November 07, 2016; Accepted date: February 10, 2017; Published date: February 27, 2017

Citation: Delgado JJ (2017) A Original Solution To The 4 Colours Theorem. J Generalized Lie Theory Appl 11:258. doi:10.4172/1736-4337.1000258

### Abstract

Definition of theorem: On a politic map, the neighbour countries can not to take the same colour because they could seem the same country. When the frontier between countries is a point, we must not consider it as a frontier. This is possible with three and five colours, it is proved, but with four at this moment lack an evident proof, without pc. There are infinite maps where the solution must to run, also inside of them it must to solve the relation between infinite and only four colours. For that I transform politic maps into maps in the plane graph, then I use their polygons to create other new polygons, with a particular centre. Then the group of new polygons form a structure, which distribute all points in two independent substructures, the Centres and the Crowns. This particular centre is the common vertex of some polygons belonging to plane graph, and they form a new polygon. The points which surround the centre constitute a barrier that impede the direct relation between the centre and other points. I call crown to this barrier. Each polygon is linked with the previous, so it achieves shape of spiral. Also it achieves independence among centres, and the points of the same crown do not entwine, their relations are consecutives, two by two. To specify the new structure group points in two substructures, the Centres and the Crowns, one colour goes to the centres, and three to the crowns. On the crown there is a process of colours run on a finite number of points chosen by triangulations, which impose a Stopping Condition. The triangulation happens when two or more points with two different colours have a common neighbour, then this point must to take the third colour. On each process after last triangulation happen always stopping condition, it mean that neighbour points without colours have two possibilities, and the rest three, which guarantee the resolution. The global outcome is a Big Crown biggest after each process, whose internal points and their links do not influence on the following points. There are two graphics files, Formation of structure and Plans, where I change the three colours by three shapes: triangle, circle and square. I recommend to see the two graphics files consecutively

### Related Subjects

Peer Reviewed Journals

Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2018-19

Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

### Conferences By Subject

Agri & Aquaculture Journals

Dr. Krish

+1-702-714-7001Extn: 9040

Biochemistry Journals

Datta A

1-702-714-7001Extn: 9037

Ronald

1-702-714-7001Extn: 9042

Chemistry Journals

Gabriel Shaw

1-702-714-7001Extn: 9040

Clinical Journals

Datta A

1-702-714-7001Extn: 9037

Engineering Journals

James Franklin

1-702-714-7001Extn: 9042

Food & Nutrition Journals

Katie Wilson

1-702-714-7001Extn: 9042

General Science

Andrea Jason

1-702-714-7001Extn: 9043

Genetics & Molecular Biology Journals

Anna Melissa

1-702-714-7001Extn: 9006

Immunology & Microbiology Journals

David Gorantl

1-702-714-7001Extn: 9014

Materials Science Journals

Rachle Green

1-702-714-7001Extn: 9039

Nursing & Health Care Journals

Stephanie Skinner

1-702-714-7001Extn: 9039

Medical Journals

Nimmi Anna

1-702-714-7001Extn: 9038

Neuroscience & Psychology Journals

Nathan T

1-702-714-7001Extn: 9041

Pharmaceutical Sciences Journals

Ann Jose

1-702-714-7001Extn: 9007

Social & Political Science Journals

Steve Harry

1-702-714-7001Extn: 9042

© 2008- 2018 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version