SEMINAR: Groups and Combinatorics Seminar, Metrically homogeneous graphs
|Groups and Combinatorics Seminar, Metrically homogeneous graphs
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.
Blakers Lecture Theatre G.18
Fri, 21 Feb 2014 15:00
Fri, 21 Feb 2014 16:00
Irene Pivotto <[email protected]>
Tue, 04 Mar 2014 10:48
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