On Frankl and Fredi's Conjecture for 3-uniform Hypergraphs  

作　　者：Qing-song TANG Hao PENG Cai-ling WANG Yue-jian PENG 

机构地区：[1]College of Sciences,Northeastern University [2]School of Mathematics,Jilin University [3]College of Mathematics,Hunan University

出　　处：《Acta Mathematicae Applicatae Sinica》2016年第1期95-112,共18页应用数学学报（英文版）

基　　金：Supported by Chinese Universities Scientic Fund(No.N140504004);the National Natural Science Foundation of China(No.11271116)

摘　　要：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）.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）.

关 键 词：Colex ordering Lagrangians of r-graphs extremal problems in combinatorics 

分 类 号：O157.5[理学—数学] O171[理学—基础数学]