Tuesday 26/11, Martin Doležal

[kubis at math.cas.cz]

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 Tuesday 26th November, 10:00am 
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 Speaker:Martin Doležal, IM CAS
 Title: A Turán-type theorem for large-distance graphs in Euclidean spaces

 Abstract  

 Turán’s theorem, a classical result in graph theory, provides an upper bound on the number of edges in any graph with n vertices and with no complete subgraphs on k vertices. We are interested in analogous results for so called large-distance graphs. A large-distance graph is a measurable graph whose vertex set is a measurable subset of Euclidean space, and two vertices are connected by an edge if and only if their distance is larger that 2. We ask for upper bounds on the measures of vertices and edges of a large-distance graph with no complete subgraphs on k vertices. One of our main results says that if A is a measurable subset of a plane such that the large-distance graph of A does not contain any complete subgraph on three vertices then the 2-dimensional Lebesgue measure of A is at most 2?.
 
This is a joint work with J. Hladký, J. Kolá?, T. Mitsis, C. Pelekis and V. Vlasák.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .