2013/05/06 by Vladimir Nikiforov, Nikiforov, Vladimir · 2 citations
Mathematics · #05C35 #05C65 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C35 #msc:05C65
paper · pdf · doi:10.48550/arxiv.1305.1073
31 pages, the main Theorem 12 is extended, the presentation is simplified
arxiv created 2013/05/13 · arxiv updated 2013/05/14
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently introduced graph parameter. The paper builds a basis for the systematic study of this parameter and illustrates a range of various proof tools. It is shown that extremal problems about the number of edges of uniform hypergraphs are asymptotically equivalent to extremal problems about the largest eigenvalue; this result is new even for 2-graphs. Several concrete problems are adressed and solutions to many more are suggested. A number of open problems are raised and directions for further studies are outlined.