## Tilings in vertex ordered graphs

- Feb. 26, 2021
- 2:30 p.m.

## Abstract

Over recent years there has been much interest in both Turán 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 Kühn and Osthus. 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.