On Frankl and Fredi＇s Conjecture for 3-uniform Hypergraphs
Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian of all r-graphs with m edges.Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ（G）.In this paper,we first show that if（3^t-1...
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| Published in | 应用数学学报：英文版 no. 1; pp. 95 - 112 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
2016
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| Online Access | Get full text |
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| Abstract | Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian of all r-graphs with m edges.Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ（G）.In this paper,we first show that if（3^t-1） ≤m〈（3^t）,G is a left-compressed 3-graph with m edges and on vertex set[t],the triple with minimum colex ordering in G^c is（t — 2 — i）（t — 2）t,then λ（G） ≤λ（C3,m）.As an implication,the conjecture of Frankl and Fiiredi is true for（3^t）-6≤m≤（3^t）. |
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| AbstractList | Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian of all r-graphs with m edges.Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ（G）.In this paper,we first show that if（3^t-1） ≤m〈（3^t）,G is a left-compressed 3-graph with m edges and on vertex set[t],the triple with minimum colex ordering in G^c is（t — 2 — i）（t — 2）t,then λ（G） ≤λ（C3,m）.As an implication,the conjecture of Frankl and Fiiredi is true for（3^t）-6≤m≤（3^t）. |
| Author | Qing-song TANG Hao PENG Cai-ling WANG Yue-jian PENG |
| AuthorAffiliation | College of Sciences, Northeastern University, Shenyang, 110819, China School of Mathematics, Jilin University, Changchun 130012, China College of Mathematics, Hunan University, Changsha 410082, China |
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| Notes | Colex ordering Lagrangians of r-graphs extremal problems in combinatorics 11-2041/O1 Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian of all r-graphs with m edges.Denote this r-graph by Cr,m and the Lagrangian of a hypergraph by λ（G）.In this paper,we first show that if（3^t-1） ≤m〈（3^t）,G is a left-compressed 3-graph with m edges and on vertex set[t],the triple with minimum colex ordering in G^c is（t — 2 — i）（t — 2）t,then λ（G） ≤λ（C3,m）.As an implication,the conjecture of Frankl and Fiiredi is true for（3^t）-6≤m≤（3^t）. |
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| Snippet | Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian... |
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| StartPage | 95 |
| SubjectTerms | 均匀 弗兰克 拉格朗日 排序 猜想 超图 顶点集 |
| Title | On Frankl and Fredi＇s Conjecture for 3-uniform Hypergraphs |
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