A homology theory for colored graphs Original Research Article

We introduce a homology theory for colored graphs (G, CG which is motivated by topological reasons. Indeed, it translates the usual one of the polyhedron |G| canonically associated to (G, GG). Then we obtain combinatorial analogs to exact homology sequences, cohomology groups, products, duality, etc. and prove some classic results of algebraic topology by graph-theoretic tools. Finally we study some combinatorial invariants of (G, CG) which are useful to describe the topological structure of |G|.