On a conjecture of Stein

@article{Aharoni2016OnAC,
  title={On a conjecture of Stein},
  author={R. Aharoni and E. Berger and Dani Kotlar and R. Ziv},
  journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  year={2016},
  volume={87},
  pages={203-211}
}
  • R. Aharoni, E. Berger, +1 author R. Ziv
  • Published 2016
  • Mathematics
  • Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
  • Stein (Pac J Math 59:567–575, 1975) proposed the following conjecture: if the edge set of $$K_{n,n}$$Kn,n is partitioned into n sets, each of size n, then there is a partial rainbow matching of size $$n-1$$n-1. He proved that there is a partial rainbow matching of size $$n(1-\frac{D_n}{n!})$$n(1-Dnn!), where $$D_n$$Dn is the number of derangements of [n]. This means that there is a partial rainbow matching of size about $$(1- \frac{1}{e})n$$(1-1e)n. Using a topological version of Hall’s theorem… CONTINUE READING
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