Title: Eigenvalue bounds to the (co)clique and chromatic numbers
|Affiliation:||Federal University of Minas Gerais, Brazil|
This is perhaps one of the oldest topics of interest in spectral graph theory, dating back to the works of Hoffman, Haemers, Delsarte and others, in the 70s. Nevertheless, it seems that one cannot stop to find questions to ask, and many interesting results have appeared recently. In this talk, I will survey few of my favourite old and new results, highlighting connections to semidefinite programming and quantum information theory. I will also present three results, each relating to a different type of question about the topic, and then I will discuss some of the things I have been speculating lately.
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