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                * Princeton Discrete Math Seminar *
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Speaker: Sebastian Cioaba (U. Delaware)

Thursday 13th December, 3:00 in Fine Hall 224.

Title: The smallest eigenvalues of Hamming, Johnson and other graphs

The smallest eigenvalue of a graph is closely related to other graph
parameters such as the independence number, the chromatic number or the
max-cut. In this talk, I will describe the well-known connections between
the smallest eigenvalue and the max-cut of a graph that have motivated
various researchers such as Karloff, Alon, Sudakov, Van Dam, Sotirov to
investigate the smallest eigenvalue of Hamming and Johnson graphs. I will
describe our proofs of a conjecture by Van Dam and Sotirov on the smallest
eigenvalue of (distance-j) Hamming graphs and a conjecture by Karloff on the
smallest eigenvalue of (distance-j) Johnson graphs and mention some open
problems. This is joint work with Andries Brouwer, Ferdinand Ihringer and
Matt McGinnis.

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Next week: break

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