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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Subjects | |
Online Access | Get full text |
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Summary: | 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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Bibliography: | 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). |
ISSN: | 0168-9673 1618-3932 |