At the Virtual Discrete Math Colloquium on January 13, 2021, Rose McCarty from University of Waterloo gave a talk presenting her work with Jim Geelen and Paul Wollan on flooding immersions of Eulerian group-labelled graphs, related to vertex-minors of graphs. The title of her talk was “Vertex-minors and flooding immersions“.
Rose McCarty, Vertex-minors and flooding immersions
An immersion of a graph H into a graph G sends edges of H into edge-disjoint trails of G. We say the immersion is flooding if every edge of G is in one of the trails. Flooding immersions are interesting for Eulerian group-labelled graphs; in this context they behave quite differently from regular immersions. Moreover, understanding such flooding immersions is a vital step towards understanding the structure of graphs with a forbidden vertex-minor.
I will focus on explaining the connection to vertex-minors, and on recent progress in this direction from ongoing joint work with Jim Geelen and Paul Wollan.
Rose McCarty presented her work on the chromatic number of circle graphs at the Discrete Math Seminar
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.”
Rose McCarty, 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.