Geodesic
On the Turán density of \(\{1, 3\}\)-hypergraphs
Shuliang Bai1 ; Linyuan Lu2
1Harvard University
2University of South Carolina
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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In this paper, we consider the Turán problems on $\{1,3\}$-hypergraphs. We prove that a $\{1, 3\}$-hypergraph is degenerate if and only if it's $H^{\{1, 3\}}_5$-colorable, where $H^{\{1, 3\}}_5$ is a hypergraph with vertex set $V=[5]$ and edge set $E=\{\{2\}, \{3\}, \{1, 2, 4\},\{1, 3, 5\}, \{1, 4, 5\}\}.$ Using this result, we further prove that for any finite set $R$ of distinct positive integers, except the case $R=\{1, 2\}$, there always exist non-trivial degenerate $R$-graphs. We also compute the Turán densities of some small $\{1,3\}$-hypergraphs.
DOI : 10.37236/8072
Classification : 05C65, 05D40

Shuliang Bai  1   ; Linyuan Lu  2

1 Harvard University
2 University of South Carolina 
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     title = {On the {Tur\'an} density of \(\{1, 3\}\)-hypergraphs},
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Shuliang Bai; Linyuan Lu. On the Turán density of \(\{1, 3\}\)-hypergraphs. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8072

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