# Algebra Seminar by Joanna Fawcett

On Wednesday the 27th of March 2019, Joanna Fawcett (Imperial College London) will be visiting the Charlotte Scott Centre for Algebra and giving a seminar. Her talk will be at 3pm in INB 3305. The details are as follows:

Title: 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 \textit{tree-homogeneous} if it is $X$-homogeneous where $X$ is the class of trees. We will 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.

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