
Sjanne Zeijlemaker (Eindhoven UT)  Optimization of eigenvalue bounds for the independence and chromatic number of graph powers Supervisor: Aida Abiad Recorded full presentation Abstract The kth power of a graph G is the graph in which two distinct vertices are adjacent if their distance in G is at most k. The independence number and chromatic number of a kth graph power are known as the kindependence and kchromatic number. In this talk, we prove and optimize various eigenvalue bounds for these parameters which purely depend on the spectrum of G. Our bounds for the kindependence number also work for its quantum counterpart, which is not known to be a computable parameter in general. 