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Zero-sum flows for Steiner systems
Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.disc.2020.112074
S. Akbari; H.R. Maimani; Leila Parsaei Majd; I.M. Wanless

Given a t-(v,k,λ) design, D=(X,B), a zero-sum n-flow of D is a map f:B{±1,,±(n1)} such that for any point xX, 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 v1(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.

更新日期:2020-08-01

 

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