Name
Abstract | ||
|---|---|---|
We show that every simple, (weakly) connected, possibly directed and infinite, hypergraph has a unique prime factor decomposition with respect to the (weak) Cartesian product, even if it has infinitely many factors. This generalizes previous results for graphs and undirected hypergraphs to directed and infinite hypergraphs. The proof adopts the strategy outlined by Imrich and Žerovnik for the case of graphs and introduces the notion of diagonal-free grids as a replacement of the chord-free 4-cycles that play a crucial role in the case of graphs. This leads to a generalization of relation Δ on the arc set, whose convex hull is shown to coincide with the product relation of the prime factorization. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1002/jgt.20609 | Journal of Graph Theory |
Keywords | Field | DocType |
cartesian product,wiley periodicals,arc set,inc. j graph theory,undirected hypergraphs,prime factorization,unique prime factor decomposition,product relation,chord-free 4-cycles,infinite hypergraphs,grid | Graph theory,Discrete mathematics,Graph,Combinatorics,Cartesian product,Hypergraph,Constraint graph,Convex hull,Unique prime,Prime factor,Mathematics | Journal |
Volume | Issue | ISSN |
70 | 2 | 0364-9024 |
Citations | PageRank | References |
10 | 0.71 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lydia Ostermeier | 1 | 29 | 3.98 |
| marc hellmuth | 2 | 148 | 22.80 |
| Peter F. Stadler | 3 | 1839 | 152.96 |