2013/11/06 by Qingsong Tang, Yuejian Peng, Tang, Qingsong +5 · 2 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1311.1409
20pages 5 figures. arXiv admin note: text overlap with arXiv:1211.7056, arXiv:1211.6508, arXiv:1212.2795, arXiv:1311.1062
arxiv created 2013/11/06 · arxiv updated 2013/11/07
Motzkin and Straus established a remarkable connection between the maximum clique and the Lagrangian of a graph in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique number in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we provide upper bounds on the Lagrangian of a hypergraph containing dense subgraphs when the number of edges of the hypergraph is in certain ranges. These results support a pair of conjectures introduced by Y. Peng and C. Zhao (2012) and extend a result of J. Talbot (2002). \keywordsCliques of hypergraphs \and Colex ordering \and Lagrangians of hypergraphs \and Polynomial optimization