Refined Turán numbers and Ramsey numbers for the loose 3-uniform path of length three

@article{Polcyn2017RefinedTN,
  title={Refined Tur{\'a}n numbers and Ramsey numbers for the loose 3-uniform path of length three},
  author={Joanna Polcyn and Andrzej Rucinski},
  journal={Discret. Math.},
  year={2017},
  volume={340},
  pages={107-118}
}
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We show that if we color the hyperedges of the complete $3$-uniform complete graph on $2n+\sqrt{18n+1}+2$ vertices with $n$ colors, then one of the color classes contains a loose path of length three.
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