论文信息 - On the largest graph-Lagrangians of hypergraphs

On the largest graph-Lagrangians of hypergraphs

Frankl and F\"uredi (1989) conjectured that the $r$-graph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest graph-Lagrangian of all $r$-graphs with $m$ edges. In this paper, we establish some bounds for graph-Lagrangians of some special $r$-graphs that support this conjecture.

Xiangde Zhang | Yuejian Peng | Cheng Zhao | Qingsong Tang

[1] Dhruv Mubayi,et al. A hypergraph extension of Turán's theorem , 2006, J. Comb. Theory, Ser. B.

[2] Xiangde Zhang,et al. On Graph-Lagrangians of Hypergraphs Containing Dense Subgraphs , 2014, J. Optim. Theory Appl..

[3] Marcello Pelillo,et al. A generalization of the Motzkin–Straus theorem to hypergraphs , 2009, Optim. Lett..

[4] Yuejian Peng,et al. A Motzkin–Straus Type Result for 3-Uniform Hypergraphs , 2013, Graphs Comb..

[5] Vera T. Sós,et al. Extremals of functions on graphs with applications to graphs and hypergraphs , 1982, J. Comb. Theory, Ser. B.

[6] Yuejian Peng,et al. On Lagrangians of r-uniform hypergraphs , 2015, J. Comb. Optim..

[7] Vojtech Rödl,et al. Hypergraphs do not jump , 1984, Comb..

[8] Xiangde Zhang,et al. Some results on Lagrangians of hypergraphs , 2014, Discret. Appl. Math..

[9] Marcello Pelillo,et al. A Continuous Characterization of Maximal Cliques in k-Uniform Hypergraphs , 2008, LION.

[10] Zoltán Füredi,et al. Extremal problems whose solutions are the blowups of the small witt-designs , 1989, J. Comb. Theory, Ser. A.

[11] T. Motzkin,et al. Maxima for Graphs and a New Proof of a Theorem of Turán , 1965, Canadian Journal of Mathematics.