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Article overview
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Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms | | Marc Hellmuth
; Manuel Noll
; Lydia Ostermeier
; | | Date: |
8 May 2013 | | Abstract: | It is well-known that all finite connected graphs have a unique prime factor
decomposition (PFD) with respect to the strong graph product which can be
computed in polynomial time. Essential for the PFD computation is the
construction of the so-called Cartesian skeleton of the graphs under
investigation.
In this contribution, we show that every connected thin hypergraph H has a
unique prime factorization with respect to the normal and strong (hypergraph)
product. Both products coincide with the usual strong graph product whenever H
is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as
a natural generalization of the Cartesian skeleton of graphs and prove that it
is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian
skeleton of hypergraphs can be determined in O(|E|^2) time and that the PFD can
be computed in O(|V|^2|E|) time, for hypergraphs H = (V,E) with bounded degree
and bounded rank. | | Source: | arXiv, 1305.1824 | | Services: | Forum | Review | PDF | Favorites | |
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