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The Maximum Lagrangian of 5-uniform Hypergraphs without Containing Two Edges Intersecting at a Vertex

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Abstract

Obtaining Turán densities of hypergraph through determining Lagrangian densities have been studied actively. Sidorenko showed that the Lagrangian density of an r-uniform hypergraph equals the Turán density of the extension of this hypergraph. Indeed, Lagrangian density and Turán density are the same for a large class of hypergraphs such as hypergraphs covering pairs. Let Pr,s be the r-uniform hypergraph with two edges intersecting at s vertices. Sidorenko determined the Lagrangian densities of Pr,s for r = 3 and s = 1 or 2, or r = 4 and s = 2 or 3. Hefetz and Keevash determined for r = 3 and s = 0, and Bene Watts, Norin and Yepremyan determined for r ≥ 4 and s = 0. The cases r = 5 and s = 4 or r = 6 and s = 5 were determined by Norin and Yepremyan. Jenssen showed for r = 5, 6 or 7, and s = 3, 4 or 5 respectively. The cases r = 4 and s = 1 or r = 5 and s = 2 were determined by Jiang, Peng and Wu, and Hu, Peng and Wu respectively. For r = 5, the only remaining case is s = 1. In this paper, we determine for this case.

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Acknowledgements

We thank two reviewers for reading the manuscript carefully, and giving insightful comments to help improve the manuscript.

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Authors and Affiliations

  1. MOE-LCSM, School of Mathematics and Statistics, Hu’nan Normal University, Changsha, 410081, P. R. China

    Biao Wu

  2. School of Mathematics, Hu’nan University, Changsha, 410082, P. R. China

    Yue Jian Peng

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  1. Biao Wu
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  2. Yue Jian Peng
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Correspondence to Yue Jian Peng.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11901193 and 11931002), National Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50364) and the Construct Program of the Key Discipline in Hu’nan Province

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Wu, B., Peng, Y.J. The Maximum Lagrangian of 5-uniform Hypergraphs without Containing Two Edges Intersecting at a Vertex. Acta. Math. Sin.-English Ser. 38, 877–889 (2022). https://doi.org/10.1007/s10114-022-0388-z

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  • DOI: https://doi.org/10.1007/s10114-022-0388-z

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