东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (8): 1209-1212+1216.DOI: -

• 论著 • 上一篇    下一篇

关于Frankl-Füredi猜想的一个结果

唐青松;陆小军;张祥德;朱和贵;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(10801026)

A result on the conjecture of Frankl-Füredi

Tang, Qing-Song (1); Lu, Xiao-Jun (1); Zhang, Xiang-De (1); Zhu, He-Gui (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Zhang, X.-D.
  • About author:-
  • Supported by:
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摘要： Frankl和Füredi猜测在所有边数为m的r-图中,由N(r)中Colex序最小的m个元素组成的r-图具有最大的拉格朗日极值.本文证明,对于边数为m的3-图,当[(t-1)/3]≤m≤[t-1/3]+[(t-2)/2]且t≤8时,这一猜想成立.

关键词: 超图, 拉格朗日极值, Frankl-Füredi猜想, Colex序, Turán问题

Abstract: It was conjectured by Frankl and Fu¨redi that the r-graph with m edges formed by taking the first m elements in the Colex ordering of N(r) had the largest Lagrangian of all r-graphs with m edges. In this paper, it is proved that when the following relationships are given for the 3-graph with m edges, i. e., (t-1/3)&lem&le(t-1/3)+(t-2/2) and t&le8, this conjecture will be right.

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