Abstract: Given two graphs H and G, an H-tiling in G is a collection of vertex disjoint copies of H in G. Thus, an H-tiling is simply a generalisation of the notion of a matching (which corresponds to the case when H is an edge). An H-tiling in G is perfect if every vertex of G is covered by the H-tiling.
Over the last 60 years there have been numerous results on perfect H-tilings. In this talk we give a high-level overview of some of the key ideas that permeate the topic. In particular, we will discuss some typical behaviour of extremal examples, and also some complexity questions.
