# Combinatorics Seminar 2015

Date: Wed, Apr 08, 2015

Time: 13:00 - 14:00

Venue: Middle Meeting Room

Title: Some extremal results in spectral hypergraph theory

Abstract:

We study some extremal problems in spectral hypergraph theory. Firstly we generalize some useful operations from ordinary graphs to hypergraphs. These operations include the edge-moving operation, the total grafting operation, etc. We study the perturbation of the spectral radii of hypergraphs under these operations. Using these operations, we determine the hypergraphs with the largest and second largest spectral radii in the class of all $k$-uniform supertrees with $n$ vertices. We also determine the hypergraphs with the largest and smallest spectral radii in the class of all $k$-uniform hypertrees with $n$ vertices, by using these generalized operations on hypergraphs.

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