Algebra seminar in Lincoln: talk by Dr Joanna Fawcett

Charlotte Scott Centre for Algebra

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 $latex X$ be a class of graphs. A graph $latex Gamma$ is $latex X$-homogeneous if every graph isomorphism $latex varphi:Delta_1to Delta_2$ between induced subgraphs $latex Delta_1$ and $latex Delta_2$ of $latex Gamma$ such that $latex Delta_1in X$ extends to an automorphism of $latex Gamma$. For example, if $latex X={K_1}$, then $latex X$-homogeneity is vertex-transitivity, and if $latex X={K_2}$, then $latex X$-homogeneity is arc-transitivity. A graph is tree-homogeneous if it is $latex X$-homogeneous where $latex X$ 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.

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