Abstract: Over recent years, there has been much interest in both Turan and Ramsey properties of vertex ordered graphs. In this talk, we initiate the study of embedding spanning structures into vertex ordered graphs. In particular, we introduce a general framework for approaching the problem of determining the minimum degree threshold for forcing a perfect $H$-tiling in an ordered graph. (In the unordered graph setting, this problem was resolved by Kuhn and Osthus in 2009.) We use our general framework to resolve the perfect $H$-tiling problem for all ordered graphs $H$ of interval chromatic number $2$. Already in this restricted setting the class of extremal examples is richer than in the unordered graph problem. This is joint work with Jozsef Balogh and Andrew Treglown.
Please contact Sean at SEnglish (at) illinois (dot) edu for the Zoom information.