2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102685A multi-component electron model on a lattice is constructed whose ground state exhibits a spontaneous ordering which follows the rule of map-coloring used in the solution of the four color problem. The number of components is determined by the Euler characteristics of a certain surface into which the lattice is embedded. Combining the concept of chromatic polynomials with the Heawood-Ringel-Youngs theorem, we derive an index theorem relating the degeneracy of the ground state with a hidden topology of the lattice. The system exhibits coloring transition and hidden-topological structure transition. The coloring phase exhibits a topological order.5 pages, 3 figuresStrongly Correlated ElectronsOther Condensed Mattertext