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- W1999442116 abstract "The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Lagrangian of a hypergraph. Frankl and Füredi 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. Talbot in Talbot (2002) provided some evidences for Frankl and Füredi’s conjecture. In this paper, we prove 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 -uniform graphs on t vertices with m edges when m = t r − p where 0 ≤ p ≤ t − r under some conditions. As an implication, we also derive that Frankl and Füredi’s conjecture holds for 3-uniform graphs with m = t 3 − p edges where 0 ≤ p ≤ 4 ." @default.
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- W1999442116 date "2014-03-01" @default.
- W1999442116 modified "2023-09-29" @default.
- W1999442116 title "Some results on Lagrangians of hypergraphs" @default.
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- W1999442116 doi "https://doi.org/10.1016/j.dam.2013.09.023" @default.
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