IBS/KAIST Joint Discrete Math Seminar

IBS Discrete Mathematics Group

We show that if a graph admits a $\lambda$-packing and a $\lambda$-covering then the graph also admits a decomposition into $\lambda$ many spanning trees. In this talk, we concentrate on the case of $\lambda$ being an infinite cardinal. Moreover, we will provide a new and simple proof for a theorem of Laviolette characterising the existence of a $\lambda$-packing, as well as for a theorem of Erdős and Hajnal characterising the existence of a $\lambda$-covering.

Joint work with Joshua Erde, Attila Joó, Paul Knappe and Max Pitz.