On sets of integers with restrictions on their products

@article{Tait2016OnSO,
  title={On sets of integers with restrictions on their products},
  author={Michael Tait and Jacques Verstra{\"e}te},
  journal={Eur. J. Comb.},
  year={2016},
  volume={51},
  pages={268-274}
}
A product-injective labeling of a graph G is an injection ? : V ( G ) ? Z such that ? ( u ) ? ( v ) ? ? ( x ) ? ( y ) for any distinct edges u v , x y ? E ( G ) . Let P ( G ) be the smallest N ? 1 such that there exists a product-injective labeling ? : V ( G ) ? N . Let P ( n , d ) be the maximum possible value of P ( G ) over n -vertex graphs G of maximum degree at most d . In this paper, we determine the asymptotic value of P ( n , d ) for all but a small range of values of d relative to n… Expand

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