Edge-connectivity of permutation hypergraphs

Jami, Neil; Szigeti, Zoltán

doi:10.1016/j.disc.2011.08.010

Cited by 4 publications

(3 citation statements)

References 2 publications

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“…The following result from characterizes hypergraphs that admit a k ‐edge‐connected permutation hypergraph. It generalizes Theorem and it can be proved by Theorem .…”

Section: Algorithmic Aspectsmentioning

confidence: 99%

Augmenting the Edge‐Connectivity of a Hypergraph by Adding a Multipartite Graph

Bernáth¹,

Grappe

Szigeti

2012

Journal of Graph Theory

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Given a hypergraph, a partition of its vertex set, and a nonnegative integer k, find a minimum number of graph edges to be added between different members of the partition in order to make the hypergraph k‐edge‐connected. This problem is a common generalization of the following two problems: edge‐connectivity augmentation of graphs with partition constraints (J. Bang‐Jensen, H. Gabow, T. Jordán, Z. Szigeti, SIAM J Discrete Math 12(2) (1999), 160–207) and edge‐connectivity augmentation of hypergraphs by adding graph edges (J. Bang‐Jensen, B. Jackson, Math Program 84(3) (1999), 467–481). We give a min–max theorem for this problem, which implies the corresponding results on the above‐mentioned problems, and our proof yields a polynomial algorithm to find the desired set of edges.

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“…The following result from characterizes hypergraphs that admit a k ‐edge‐connected permutation hypergraph. It generalizes Theorem and it can be proved by Theorem .…”

Section: Algorithmic Aspectsmentioning

confidence: 99%

Augmenting the Edge‐Connectivity of a Hypergraph by Adding a Multipartite Graph

Bernáth¹,

Grappe

Szigeti

2012

Journal of Graph Theory

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“…The subject of connectivity in hypergraphs has been developing recently with results like those in [1,3,6]. In [1], Bahmanian and Šajna study various connectivity properties in hypergraphs with an emphasis on cut sets of edges and vertices.…”

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confidence: 99%

“…In [3], Dewar, Pike, and Proos consider both vertex and edge-connectivity in hypergraphs with additional details on the computational complexity of these problems. In [6], Jami and Szigeti investigate the edge-connectivity of permutation hypergraphs. Dankelmann and Meierling extend several well-known sufficient conditions for graphs to be maximally edge-connected to the realm of hypergraphs in [2].…”

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confidence: 99%

The edge‐connectivity of vertex‐transitive hypergraphs

Burgess,

Luther,

Pike

2023

Journal of Graph Theory

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A graph or hypergraph is said to be vertex‐transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex‐transitive graph is maximally edge‐connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex‐transitive hypergraph is maximally edge‐connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex‐transitive hypergraphs which are not maximally edge‐connected.

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Edge-connectivity in hypergraphs

Zhao

Meng

2021

Indian J Pure Appl Math

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Edge-connectivity of permutation hypergraphs

Cited by 4 publications

References 2 publications

Augmenting the Edge‐Connectivity of a Hypergraph by Adding a Multipartite Graph

Augmenting the Edge‐Connectivity of a Hypergraph by Adding a Multipartite Graph

The edge‐connectivity of vertex‐transitive hypergraphs

Edge-connectivity in hypergraphs

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