@article {IOPORT.06047052,
    author       = {Chen, Yong-Gao and Hu, Cui-Ying},
    title        = {On a problem of Erd\H{o}s, Herzog and Sch\"onheim.},
    year         = {2012},
    journal      = {Discrete Applied Mathematics},
    volume       = {160},
    number       = {10-11},
    issn         = {0166-218X},
    pages        = {1501-1506},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.dam.2012.02.013},
    abstract     = {Summary: Let $p_{1},p_{2},\ldots ,p_{n}$ be distinct primes. In 1970, {\it P. Erd\H{o}s}, {\it M. Herzog} and {\it J. Sch\"onheim} [Isr. J. Math. 8, 408--412 (1970; Zbl 0217.30701)] proved that if $\cal D, |\cal D|=m$, is a set of divisors of $N=p^{\alpha _{1}}_{1} \cdots p^{\alpha _{n}}_{n}\ge \alpha _{1}\ge \cdots \ge \alpha _{n}$, no two members of the set being coprime and if no additional member may be included in $\cal D$ without contradicting this requirement then $m\ge\alpha_{n}\prod_{i=1}^{n-1}(\alpha_{i}+1)$. They asked to determine all sets $\cal D$ such that the equality holds. In this paper we solve this problem. We also pose several open problems for further research.},
    identifier   = {06047052},
}