Algebra seminar in Lincoln: talk by Dr Joanna Fawcett

On the 27th of March 2019, Dr Joanna Fawcett (Imperial College, London) visited Charlotte Scott Centre for Algebra in Lincoln and gave a talk on “Tree-homogeneous graphs”.

Abstract: Let $X$ be a class of graphs. A graph $\Gamma$ is $X$ -homogeneous if every graph isomorphism $\varphi:\Delta_1\to \Delta_2$ between induced subgraphs $\Delta_1$ and $\Delta_2$ of $\Gamma$ such that $\Delta_1\in X$ extends to an automorphism of $\Gamma$ . For example, if $X=\{K_1\}$ , then $X$ -homogeneity is vertex-transitivity, and if $X=\{K_2\}$ , then $X$ -homogeneity is arc-transitivity. A graph is tree-homogeneous if it is $X$ -homogeneous where $X$ is the class of trees. We discuss some recent progress on classifying the finite tree-homogeneous graphs, as well as some connections with certain highly symmetric incidence geometries called partial linear spaces.