The Cartesian product of hypergraphs

Ostermeier, Lydia; Hellmuth, Marc; Stadler, Peter F.

doi:10.1002/jgt.20609

Cited by 13 publications

(14 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Cartesian product of hypergraphs has been investigated by several authors since the 1960s [37,38,11,9,10,17,49,53]. It is probably the best-studied construction.…”

Section: The Cartesian Productmentioning

confidence: 99%

See 1 more Smart Citation

A Survey on Hypergraph Products

2012

Self Cite

View full text Add to dashboard Cite

Erratrum: In the accepted version of this survey [36] it is mistakenly stated that the direct products ⌢ × and × and the strong product ⌢ ⊠ are associative. In [32], we gave counterexamples for these cases and proved associativity of the hypergraph productsAbstract. A surprising diversity of different products of hypergraphs have been discussed in the literature. Most of the hypergraph products can be viewed as generalizations of one of the four standard graph products. The most widely studied variant, the so-called square product, does not have this property, however. Here we survey the literature on hypergraph products with an emphasis on comparing the alternative generalizations of graph products and the relationships among them. In this context the so-called 2-sections and L2-sections are considered. These constructions are closely linked to related colored graph structures that seem to be a useful tool for the prime factor decompositions w.r.t. specific hypergraph products. We summarize the current knowledge on the propagation of hypergraph invariants under the different hypergraph multiplications. While the overwhelming majority of the material concerns finite (undirected) hypergraphs, the survey also covers a summary of the few results on products of infinite and directed hypergraphs. Mathematics Subject Classification (2000). Primary 99Z99; Secondary 00A00.

show abstract

“…The Cartesian product of hypergraphs has been investigated by several authors since the 1960s [37,38,11,9,10,17,49,53]. It is probably the best-studied construction.…”

Section: The Cartesian Productmentioning

confidence: 99%

“…Theorem 16.1 (UPFD [49]). Every simple connected finite or infinite hypergraph with finitely or infinitely many factors has a unique PFD w.r.t.…”

Section: Infinite Hypergraphsmentioning

confidence: 99%

A Survey on Hypergraph Products

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…But for cyclic structured graphs, the shortest distance ( , V) naturally is not equal to the longest distance ( , V). In this paper, the new index which is Gutman index of graphs with Figure 1 respect to detour distance [7,8] is considered; this is named as Detour Gutman index which is defined as Gut…”

Section: Introductionmentioning

confidence: 99%

Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs

Kavithaa

Kaladevi²

2017

Journal of Applied Mathematics

View full text Add to dashboard Cite

The Gutman index of a connected graph is defined as Gut( ) = ∑ ̸ =V ( ) (V) ( , V), where ( ) and (V) are the degree of the vertices and V and ( , V) is the distance between vertices and V. The Detour Gutman index of a connected graph is defined as Gut( ) = ∑ ̸ =V ( ) (V) ( , V), where ( , V) is the longest distance between vertices and V. In this paper, the Gutman index and the Detour Gutman index of pseudo-regular graphs are determined.

show abstract

“…If t(e) = h(e) for all e ∈ E the hypergraph is called undirected and directed, otherwise. Products of hypergraphs have been investigated by several authors since the 1960s [2,3,5,6,7,8,10,16,19,20,22,23,25,28,32]. It was shown by Imrich [19] that connected undirected hypergraphs have a unique prime factor decomposition (PFD) w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Fast factorization of Cartesian products of (directed) hypergraphs

Hellmuth

Lehner

2016

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique prime factor decomposition (PFD) results with respect to the Cartesian product are known. However, there is still a lack of algorithms, that compute the PFD of directed hypergraphs with respect to the Cartesian product.In this contribution, we focus on the algorithmic aspects for determining the Cartesian prime factors of a finite, connected, directed hypergraph and present a first polynomial time algorithm to compute its PFD. In particular, the algorithm has time complexity O(|E||V|r 2 ) for hypergraphs H = (V, E), where the rank r is the maximum number of vertices contained in an hyperedge of H. If r is bounded, then this algorithm performs even in O(|E| log 2 (|V|)) time. Thus, our method additionally improves also the time complexity of PFD-algorithms designed for undirected hypergraphs that have time complexity O(|E||V|r 6 ∆ 6 ), where ∆ is the maximum number of hyperedges a vertex is contained in.

show abstract

The Cartesian product of hypergraphs

Cited by 13 publications

References 16 publications

A Survey on Hypergraph Products

A Survey on Hypergraph Products

Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs

Fast factorization of Cartesian products of (directed) hypergraphs

Contact Info

Product

Resources

About