Further 6-sparse Steiner Triple Systems

Forbes, Anthony D.; Grannell, M. J.; Griggs, T. S.

doi:10.1007/s00373-008-0819-3

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Sparse Steiner Systems1

Introduction1

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2009

2013

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Cited by 2 publications

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“…Wolfe [68,70] Forbes, Grannell and Griggs [31,32] constructed infinite classes of 6-sparse STS(n)'s. As Teirlinck [66] writes in his 2009 review of [70] "currently no nontrivial example of a 7-sparse Steiner triple system is known".…”

Section: Sparse Steiner Systemsmentioning

confidence: 99%

Uniform hypergraphs containing no grids

Füredi¹,

Ruszinkó²

2013

Advances in Mathematics

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A hypergraph is called an r × r grid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e., a family of sets {A 1 , . . . , A r , B 1 , . . . , B r } such thatA hypergraph is linear, if |E ∩ F | ≤ 1 holds for every pair of edges.In this paper we construct large linear r-hypergraphs which contain no grids. Moreover, a similar construction gives large linear r-hypergraphs which contain neither grids nor triangles.For r ≥ 4 our constructions are almost optimal. These investigations are also motivated by coding theory: we get new bounds for optimal superimposed codes and designs. *

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Section: Sparse Steiner Systemsmentioning

confidence: 99%

Uniform hypergraphs containing no grids

Füredi¹,

Ruszinkó²

2013

Advances in Mathematics

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“…Although substantial progress has been made by Fujiwara [7,8] and by Wolfe [15][16][17], the proof is still incomplete. As regards 6-sparse systems, infinitely many of these are known [4,5], but no non-trivial k-sparse systems are known for any k ≥ 7.…”

Section: Introductionmentioning

confidence: 99%