The gap between 1/2 and the sum of squared Perron vector entries on an independent set can be exponentially small in graphs with arbitrarily large chromatic number, disproving two conjectures.
Cioab˘ a, The principal eigenvector of a connected graph, in: Spectral Graph Theory Online Conference, (2021),http://spectralgraphtheory.org/sgt-online-program
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An exponentially small gap of the Perron vector on independent sets
The gap between 1/2 and the sum of squared Perron vector entries on an independent set can be exponentially small in graphs with arbitrarily large chromatic number, disproving two conjectures.