Perfect Clar structures and 3-homogeneous simplicial complexes

In this paper we discuss the notion of a Clar structure on a 3-homogeneous simplicial complex, in particular on a triangulated surface. Such structures arise in theoretical chemistry, from where they also have received the name. We discuss various aspects of Clar structures, particularly existence of Clar structures on (closed compact) surfaces of general genus, and a possible variation of the definition using a splitting. We give an interpretation of Clar structures in terms of (mod 2) two step homology groups, which establishes the relationship of these structures with certain standard calculations in algebraic topology.