Hopf algebra methods in graph theory Original Research Article

We study invariants of graphs, matroids and other combinatorial objects by considering certain associated Hopf algebras. We prove a structure theorem for these Hopf algebras which implies that any invariant which counts subobjects of a particular type is given by a unique polynomial in invariants which count connected subobjects. We introduce an invertible transformation between the set of all such invariants and the set of additive invariants.