Graph decompositions using group actions

Abstract: I will present some recent results on graph decompositions. To this end, we find a very `nice’ subgraph H in a host graph we would like to decompose into copies of H. Then we employ a group action to `rotate’ H. This rotation yields a decomposition of the host graph into copies of H. We construct this `nice’ subgraph using probabilistic tools, a well-known hypergraph matching theorem due to Pippenger and Spencer and an absorption method. This is joint work with Stefan Ehard and Stefan Glock.