Geodesic
On the Erd{\H o}s--Hajnal problem in the case of $3$-graphs
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XI, Tome 488 (2019), pp. 168-176

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Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph which is not $r$-colorable. For the broad history of the problem see [10]. It is known [4] that for a fixed $n$ the sequence $$ \frac{m(n,r)}{r^n} $$ has a limit. The only trivial case is $n=2$ in which $m(2,r) = \binom{r+1}{2}$. In this note we focus on the case $n=3$. First, we compare the existing methods in this case and then improve the lower bound. 
@article{ZNSL_2019_488_a7,
     author = {D. D. Cherkashin},
     title = {On the {Erd{\H} {o}s--Hajnal} problem in the case of $3$-graphs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--176},
     publisher = {mathdoc},
     volume = {488},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_488_a7/}
}
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D. D. Cherkashin. On the Erd{\H o}s--Hajnal problem in the case of $3$-graphs. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XI, Tome 488 (2019), pp. 168-176. http://geodesic.mathdoc.fr/item/ZNSL_2019_488_a7/