Planar Graph Homologies and the 4-Color Theorem.

Jyothiniranjan Pillay (1, 2)

1 IFoA - Institute and Faculty of Actuaries Scotland
2 Microsoft Corporation [Redmond]

We introduce a Planar-Graph homology with the aim of simplifying the algebra as-sociated with the establishment of minimal coloring associated with planar-graphs. We then use the theory introduced to propose a simple proof of the 4-color theorem. Finally we introduce a proposed relation between information exposed via a chosen homology and others forming a basis for a new platform.

Mots clés: 4-color Theorem; coloring; 4-color Theorem

Domaines: Mathématiques générales [math.GM]

Jyothiniranjan Pillay. Planar Graph Homologies and the 4-Color Theorem.. 2008. ⟨hal-00655056v3⟩