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“.
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 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.