Lagrangians of Hypergraphs
Lagrangians of Hypergraphs
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DOI：
10.1017/s0963548301005053
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发表时间：
2002-03
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影响因子：
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通讯作者：
John M. Talbot
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文献类型：
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作者：
John M. Talbot
How large can the Lagrangian of an r-graph with m edges be? Frankl and Füredi [1] conjectured that the r-graph of size m formed by taking the first m sets in the colex ordering of N(r) has the largest Lagrangian of all r-graphs of size m. We prove the first ‘interesting’ case of this conjecture, namely that the 3-graph with (t3) edges and largest Lagrangian is [t](3). We also prove that this conjecture is true for 3-graphs of several other sizes. For general r-graphs we prove a weaker result: for t sufficiently large, the r-graph of size (tr) supported on t + 1 vertices and with largest Lagrangian, is [t](r).
