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 -