Lies Beers (Vrije Universiteit Amsterdam, Hollandia): At the end of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian.

Április 11-én  a Kombinatorika szemináriumon (14:15, Nagyterem)

Lies Beers (Vrije Universiteit Amsterdam, Hollandia)

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At the end of the spectrum: Chromatic bounds
for the largest eigenvalue of the normalized Laplacian.

címmel

Abstract:
For a graph with largest normalized Laplacian
eigenvalue lambda and (vertex) coloring number chi, it is known that
lambda is 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.

Finally, we give upper bounds on lambda in terms of chi.