Blueprint for a Classic Proof of the Four Colour Theorem
| dc.creator | Labarque, Patrick | |
| dc.date | 2008-01-30 | |
| dc.date | 2008-08-23 | |
| dc.date.accessioned | 2026-07-07T09:57:44Z | |
| dc.date.available | 2026-07-07T09:57:44Z | |
| dc.description | The proof uses the property that the vertices of a triangulated planar graph can be four coloured if the triangles can have a +1 or -1 orientation so that the sum of the triangle orientations around each vertex is a multiple of 3. Such orientation is first used separately on one of the two triangulated polygons resulting from a Hamilton circuit in a triangulated planar graph with v vertices. The graph is then reconstructed by adding the triangles of the other polygon one by one. When the graph is totally reconstructed there is always a combination for the orientations of the triangles for which their sum around each of v-2 successive vertices in the Hamilton circuit is a multiple of 3. It is then provable that the sum of the triangle orientations around the two remaining vertices must also be a multiple of 3. | |
| dc.description | 14 pages, 8 colourfull illustrations. The hocus-pocus of the trio's is replaced by an oriented pairs invariance | |
| dc.identifier | https://arxiv.org/abs/0802.1535 | |
| dc.identifier | http://arxiv.org/abs/0802.1535 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167457 | |
| dc.subject | General Mathematics | |
| dc.title | Blueprint for a Classic Proof of the Four Colour Theorem | |
| dc.type | text |