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Zero-sum flows for Steiner systems

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2020.112074
  3. Publisher: Elsevier B.V , 2020
  4. Abstract:
  5. Given a t-(v,k,λ) design, D=(X,B), a zero-sum n-flow of D is a map f:B⟶{±1,…,±(n−1)} such that for any point x∈X, the sum of f over all blocks incident with x is zero. For a positive integer k, we find a zero-sum k-flow for an STS(uw) and for an STS(2v+7) for v≡1(mod4), if there are STS(u), STS(w) and STS(v) such that the STS(u) and STS(v) both have a zero-sum k-flow. In 2015, it was conjectured that for v>7 every STS(v) admits a zero-sum 3-flow. Here, it is shown that many cyclic STS(v) have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems. © 2020 Elsevier B.V
  6. Keywords:
  7. Steiner quadruple system ; Steiner triple system ; Zero-sum flow
  8. Source: Discrete Mathematics ; Volume 343, Issue 11 , 2020
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0012365X20302600