2019
DOI: 10.37236/8072
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On the Turán Density of $\{1, 3\}$-Hypergraphs

Abstract: 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 His 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.

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Cited by 2 publications
(29 citation statements)
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“…2. For any 2-colored bipartite graph H, π(H) 3 2 . Before proceeding to the proof, we see several important 2-colored graphs whose Turán density achieves value 3 2 , and we will use these results to prove Lemma 9.…”
Section: Turán Density Of Bipartite 2-colored Graphsmentioning
confidence: 99%
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“…2. For any 2-colored bipartite graph H, π(H) 3 2 . Before proceeding to the proof, we see several important 2-colored graphs whose Turán density achieves value 3 2 , and we will use these results to prove Lemma 9.…”
Section: Turán Density Of Bipartite 2-colored Graphsmentioning
confidence: 99%
“…An interesting problem is what the degenerate non-uniform hypergraph look like? In [3], we prove that except for the case R = {1, 2}, there always exist nontrivial degenerate R-graphs for any set R of two distinct positive integers. The degenerate {1, 3}-graphs are characterized in [3], what about the the degenerate {2, 3}-graphs?…”
Section: Introductionmentioning
confidence: 99%
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