Block-avoiding point sequencings of arbitrary length in Steiner triple systems

07/09/2019

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by   Douglas R. Stinson, et al.

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An ℓ-good sequencing of an STS(v) is a permutation of the points of the design such that no ℓ consecutive points in this permutation contain a block of the design. We prove that, for every integer ℓ≥ 3, there is an ℓ-good sequencing of any STS(v) provided that v is sufficiently large. We also prove some new nonexistence results for ℓ-good sequencings of STS(v).