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 be a class of graphs. A graph is -homogeneous if every graph isomorphism between induced subgraphs and of such that extends to an automorphism of . For example, if , then -homogeneity is vertex-transitivity, and if , then -homogeneity is arc-transitivity. A graph is *tree-homogeneous* if it is -homogeneous where 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.

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