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On Motzkin-Straus Type of Results and Frankl-F\'uredi Conjecture for Hypergraphs
- Publication Year :
- 2013
-
Abstract
- A remarkable connection between the order of a maximum clique and the Graph-Lagrangian of a graph was established by Motzkin and Straus in 1965. This connection and its extension were useful in both combinatorics and optimization. Since then, Graph-Lagrangian has been a useful tool in extremal combinatorics. In this paper, we give a parametrized Graph-Lagrangian for non-uniform hypergraphs and provide several Motzkin-Straus type results for nonuniform hypergraphs which generalize results from [1] and [2]. Another part of the paper concerns a long-standing conjecture of Frankl-F\"uredi on Graph-Lagrangians of hypergraphs. We show the connection between the Graph-Lagrangian of $\{1, r_1, r_2, \cdots, r_l\}$-hypergraphs and $\{ r_1, r_2, \cdots, r_l\}$-hypergraphs. Some of our results provide solutions to the maximum value of a class of polynomial functions over the standard simplex of the Euclidean space.<br />Comment: 24 pages
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1312.3034
- Document Type :
- Working Paper