TY - JOUR

T1 - Zero-sum flows for Steiner systems

AU - Akbari, S.

AU - Maimani, H. R.

AU - Parsaei Majd, Leila

AU - Wanless, I. M.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Steiner quadruple system

KW - Steiner triple system

KW - Zero-sum flow

UR - http://www.scopus.com/inward/record.url?scp=85088983381&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2020.112074

DO - 10.1016/j.disc.2020.112074

M3 - Article

AN - SCOPUS:85088983381

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 11

M1 - 112074

ER -