An Algebraic Perspective on Perfect Graphs - Theory Seminar

Explore an in-depth theory seminar on the algebraic perspective of perfect graphs presented by Cemil Dibek from Princeton University. Delve into the concept of sos-perfectness and its relationship to graph perfectness. Learn about the Motzkin-Straus theorem and its implications for a quartic form pG(x) defined for graphs. Discover the equivalence between perfect graphs and sos-perfect graphs, and understand how this connection, combined with the strong perfect graph theorem, leads to an explicit infinite family of nonnegative polynomials that are not sum of squares. Gain insights into graph theory, algebraic methods, and their intersections in this 42-minute lecture, recorded on October 22, 2019, with closed captions available.