ACO The ACO Seminar (2018–2019)

April 18, 3:30pm, Wean 8220
Sebastian Cioaba, University of Delaware
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-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.

Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.

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