Analytic methods for uniform hypergraphs

By Vladimir Nikiforov. 2013

94 citations recorded by the source corpus.

This paper develops analityc methods for investigating uniform hypergraphs. Its starting point is the spectral theory of 2-graphs, in particular, the largest and the smallest eigenvalues of 2-graphs. On the one hand, this simple setup is extended to weighted r-graphs, and on the other, the eigenvalues-numbers are generalized to eigenvalues-functions, which encompass also other graph parameters like Lagrangians and number of edges. The resulting theory is new even for 2-graphs, where well-settled topics become challenges again. The paper covers a multitude of topics, with more than a hundred concrete statements to underpin an analytic theory for hypergraphs. Essential among these topics are a Perron-Frobenius type theory and methods for extremal hypergraph problems. Many open problems are raised and directions for possible further research are outlined.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/033a765f6d51947886cf60ed0d7c0c54f25de811

Citations in the corpus

• Connected Hypergraphs with Small Spectral Radius (2014, unknown): “ generalize the spectra of the adjacency matrices base on the Raileigh principle of extremal eigenvalues (for example, Lim [13], Qi [18, 19], Cooper-Dutle [5], Keevash-Lenz-Mubayi [10], and Nikiforov [17], etc.) Let’s use the notion of [10, 17]. Given a hypergraph H, the polynomial form PH(x): Rn →R”