Combinatorics Seminar

Friday, November 02, 2018 at 4:15pm to 5:15pm

Microsoft Research, First Floor Conference Center, One Memorial Drive, Cambridge, MA

SPEAKER:  Sebastian Cioaba  (University of Delaware)

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


The smallest eigenvalue of graphs 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 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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