An Isoperimetric Method in Additive Theory

Hamidoune, Yahya Ould

doi:10.1006/jabr.1996.0028

Cited by 39 publications

(57 citation statements)

References 4 publications

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“…Applications of these concepts may be found in [19,[21][22][23] and in the survey paper by Serra [34]. The corresponding notion for edge connectivity was independently investigated by van den Heuvel and Jackson [26] and by the authors of [25].…”

Section: Terminology and Preliminariesmentioning

confidence: 97%

“…The present formulation used in [19,20] is more suitable for applications. A minimum cutset T is a cutset T with |T| = .…”

Section: Terminology and Preliminariesmentioning

confidence: 98%

“…The notions k-isoperimetric connectivity and k-atoms introduced by Hamidoune in [19] gives a formalism to go more deeply than the traditional connectivity. Applications of these concepts may be found in [19,[21][22][23] and in the survey paper by Serra [34].…”

Section: Terminology and Preliminariesmentioning

confidence: 99%

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Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

2011

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A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let be a vertex-transitive graph of degree d with order at least d +4. We give necessary and sufficient conditions for the vosperianity of . Moreover, assuming that distinct vertices have distinct neighbors, we show that is vosperian if and only if it is superconnected. Let G be a group and let

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Section: Terminology and Preliminariesmentioning

confidence: 97%

“…The present formulation used in [19,20] is more suitable for applications. A minimum cutset T is a cutset T with |T| = .…”

Section: Terminology and Preliminariesmentioning

confidence: 98%

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Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

2011

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“…Before proceeding with the proof and for the sake of clarity, it will be useful and efficient to introduce the needed vocabulary from the isoperimetric method (the reader interested in a general introduction to this subject is referred to [8,9]). Doing so should make easier the forthcoming references to results from the isoperimetric method in the literature.…”

Section: Lemma 32 Let a Be A Generating Subset Of A Finite Abelian mentioning

confidence: 99%

A new critical pair theorem applied to sum-free sets in Abelian groups

Hamidoune¹,

Plagne²

2004

Comment. Math. Helv.

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Abstract. We shall prove a new generalization of Vosper critical pair theorem to finite Abelian groups. We next apply this new tool to the theory of (k, l)-free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal (k, l)-free sets and determine the maximal cardinality of such a set. This result allows us for instance to give precisions on an old result of Yap: we are able to describe completely the maximal sum-free sets with cardinality at least one third of that of the ambient group.

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“…And when G is an arbitrary finite abelian group, we should turn to the extremely complicated recursive classification of Kemperman [14]. (A few years ago the problem was solved for torsion-free nonabelian groups [6], [13].) 344 Y. F. Bilu, V. F. Lev, and I.…”

Section: Introductionmentioning

confidence: 99%