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Friday, 24 May 2024 - 14:00 to 15:30 <br />
Place: IM, konÃrna
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Speaker: John K Truss, University of Leeds<br />
Title: COUNTABLE HOMOGENEOUS ORDERED BIPARTITE GRAPHS
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Abstract <br />
<p>The classification of the countable homogeneous bipartite graphs is rather straightforward; they are empty or complete, perfect matching or its complement,</p><p> and generic. Chernikov and Kruckmann asked what happens if a linear order is imposed on the structure. This is relevant (and required) in</p><p> structural Ramsey theory: the Nesetril-Rodl Theorem requires the universe of the structure to be linearly ordered. I present a solution to this, which while</p><p> not so very complicated, does require some tricks, and a rather longer list of structures. One would really like to address the same question for multipartite</p><p> graphs. I shall briefly recall the classification of the countable homogeneous multipartite graphs (with a fixed finite number of parts), in joint work</p><p> with Jenkinson and Seidel. The extension to linearly ordered multipartite graphs would require further work.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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