At both ends of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian

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• Lies Beers (Vrije Universiteit Amsterdam)
• Thursday 15 August 2024, 11:00-12:00
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HTA - Hypergraphs: Theory and Applications

For a graph with largest normalized Laplacian eigenvalue lambda and (vertex) coloring number chi, lambda is known to be larger than or equal to chi/(chi-1). We consider properties of graphs for which this bound is sharp, and we study the multiplicity of chi/(chi-1). We also look at the spectrum of the 1-sum (a graph operation) of two graphs, with a focus on the maximal eigenvalue. We consider a generalization of the bound for hypergraphs and consider uniform hypergraphs for which this bound is sharp. Finally, we study a hypergraph operation and its relation to the hypergraph bound.

This talk is part of the Isaac Newton Institute Seminar Series series.

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