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arXiv · 1305.1073

An analytic theory of extremal hypergraph problems

Vladimir Nikiforov
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Abstract

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.

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Vladimir Nikiforov. 2013-05-06. An analytic theory of extremal hypergraph problems. https://arxiv.org/abs/1305.1073

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