C&O PhD student James Davies is a recipient of the Faculty of Mathematics Graduate Research Excellence Award. James was nominated for his paper Vertex-minor-closed classes are chi-bounded which has been accepted for publication in Combinatorica.
The main result of the paper solves a conjecture of Professor Jim Geelen from 2009, that every class of graphs that is closed under taking vertex-minors is chi-bounded. Geelen's conjecture was motivated by a deeper suspicion that vertex-minor-closed classes of graphs are highly structured, and he expected that one would need to uncover that structure in order to prove the result. However, Davies was able to prove the result in full generality. His approach relied on techniques of Chudnovsky, Scott and Seymour on induced subgraphs. Geelen remarked that "the proof itself is a tour de force in combinatorial reasoning" and that Davies' theorem "is a truly outstanding result".
The Faculty of Mathematics Graduate Research Excellence Award is designed to recognize and celebrate research excellence. Two awards valued at $5,000 each will be provided annually to graduate students who are registered full time in the Faculty of Mathematics.