Homology and Hypergraph Acyclicity: A Combinatorial Invariant For Hypergraphs
Allen Parks, Stephen Leon Lipscomb · 1991
The natural associations from finite hypergraphs and simple graphs to finite simplicial complexes are used to produce new hypergraph and graph invariants. This correspondence shows that alpha-acyclic hypergraphs and chordal graphs map to homologically acyclic complexes. A new degree of hypergraph acyclicity (h-acyclicity where the h keys homology) is introduced. It is shown that alpha-acyclic yields h-acyclic, and an example is given to show that this implication is not reversible. Application of these results to database design is discussed and a conjecture characterizing h-acyclic database schemes is stated.