University of Leeds


Combinatorics of
ArcTransitive Graphs and
Partial Orders


August 2nd, 3rd 2007


A 2day meeting was held at the University of Leeds on August 2nd and 3rd 2007, entitled 'Combinatorics of ArcTransitive Graphs and Partial Orders'. This was part of the EPSRC research grant 'Combinatorics of arctransitive graphs and partial orders', and was also supported by the London Mathematical Society. There were some grants available to support attendance by UKbased research students. Accommodation was in Lyddon Hall, on the university campus. The following was the programme, with 9 main lectures and four shorter contributed talks by research students.
Thursday August 2nd 10.30 coffee 1111.55 Manfred Droste (University of Leipzig) On homogeneous Chu spaces and graphs. 12.101.05 Robert Gray (University of Leeds) On connectedhomogeneity in graphs and partial orders 1.152.15 lunch 2.303 Jo De La Rue (University of East Anglia) Constructing continuum many primitive, unbalanced countable digraphs. 3.053.35 David Knipe (University of Leeds) Some properties of the generic partial order. 3.404.35 Simon Smith (Oxford University) The structure of locally finite highly arctransitive digraphs. 4.405.10 tea 5.156.10 Norbert Seifter (Leoben) Reachability relations in transitive digraphs. dvi file Friday August 3rd 9.3010.25 Daniela Amato ( The Queen's College, Oxford) Infinite primitive highly arctransitive digraphs. 10.3010.55 coffee 1111.50 Nik Ruskuc (University of St Andrews) Endomorphism monoids of graphs and partial orders. 1212.50 James Mitchell (University of St Andrews) Continuous mappings vs. Lipschitz mappings. 12 lunch 2.052.35 Yann Peresse (University of St Andrews) Generating sequences of functions. 2.403.10 Debbie Lockett (Queen Mary, University of London), Partial orders, homomorphisms, and homogeneity. 3.154.10 Rögnvaldur G. Möller (University of Iceland) Dynamics of graph automorphisms and metric ends. 4.154.45 tea 4.505.45 Cheryl Praeger (University of Western Australia, Perth) sarctransitivity and local sarctransitivity for graphs.
Abstract for Rögnvaldur G. Möller's lecture: The behavior of an automorphism of a graph can be described in terms of its action on the end boundary. The definition of an end of a graph can be extended in various ways, for instance there are the concepts of metric ends and also the concept of bfibers. Various questions and properties of automorphisms will be discussed in relation to these concepts. This is joint work with Bernhard Kron, The University of Hamburg.
There were 33 participants, of whom 9 were research students. The conference was intended as a contribution to the research and interaction arising from a threeyear EPSRC grant held by J K Truss and H D Macpherson in the area of the title, and two of the main speakers, Droste and Praeger, were in Leeds for over a week for collaboration with Truss and Macpherson, and the postdoctoral assistant Robert Gray.
The main topic of the meeting was arctransitive graphs and partial orders, though some of the talks ranged a little more widely than that (mainly the ones from St Andrews, who are interested in related fields). The field subdivides into the study of finite and infinite examples, corresponding to the main interests of Praeger and Droste respectively, and this was reflected in the talks given. The intention was however that there should be interaction between the two, and although the methods are rather different (infinite combinatorics on the one hand, and use of the theory of finite permutation groups and the classification of finite simple groups on the other) there was valuable discussion reflecting both, and possible relations between them, for instance in the locally finite situation, and depending on the the number of ends of a graph.

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