On the largest graph-Lagrangians of hypergraphs

Qingsong Tang; Yuejian Peng; Xiangde Zhang; Cheng Zhao

On the largest graph-Lagrangians of hypergraphs

Combinatorics 2014-08-26 v2

Authors: Qingsong Tang , Yuejian Peng , Xiangde Zhang , Cheng Zhao

Abstract

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.

Keywords

hypergraph theory graph theory random graphs

Cite

@article{arxiv.1311.1062,
  title  = {On the largest graph-Lagrangians of hypergraphs},
  author = {Qingsong Tang and Yuejian Peng and Xiangde Zhang and Cheng Zhao},
  journal= {arXiv preprint arXiv:1311.1062},
  year   = {2014}
}

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