Rose McCarty from University of Waterloo presented her recent breakthrough on the polynomially 𝜒-boundedness of circle graphs at the Discrete Math Seminar on April 26, 2019 . The title of her talk was “circle graphs are polynomially chi-bounded.”
Circle graphs are the intersection graphs of chords on a circle; vertices correspond to chords, and two vertices are adjacent if their chords intersect. We prove that every circle graph with clique number k has chromatic number at most $4k^2$. Joint with James Davies.