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SEMINAR: Groups and Combinatorics Seminar, Metrically homogeneous graphs

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Today's date is Thursday, February 25, 2021
Groups and Combinatorics Seminar, Metrically homogeneous graphs Other events...
Dugald MacPherson (University of Leeds)

will speak on

Metrically homogeneous graphs

at 3pm Friday February the 21st in Blakers Lecture Theatre.


A `homogeneous structure' is a countably infinite relational structure M (e.g. graph, k-uniform hypergraph, digraph,...) with the property that every isomorphism between finite induced substructures of M extends to an automorphism of M. These are constructed by an amalgamation method developed by Fraisse (and independently Jonsson) in the 1950s. There are classification results, often very hard, in restricted contexts (e.g. graphs, partial orders, digraphs, totally ordered graphs) but in general classification seems out of reach.

I will discuss an attempt to classify `metrically homogeneous graphs', that is, countably infinite graphs M which become homogeneous when enriched by binary `distance relations' corresponding to graph-distance in M. This notion generalises distance transitivity for countably infinite graphs. Cherlin has produced a `catalogue' of metrically homogeneous graph and conjectures that it is complete. In joint work in progress with Amato and Cherlin, we verify the conjecture for metrically homogeneous graphs of diameter at most three.
Location Blakers Lecture Theatre G.18
Contact Irene Pivotto <[email protected]>
Start Fri, 21 Feb 2014 15:00
End Fri, 21 Feb 2014 16:00
Submitted by Irene Pivotto <[email protected]>
Last Updated Tue, 04 Mar 2014 10:48
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