IBS/KAIST Joint Discrete Math Seminar

A Cantor-Bernstein-type theorem for spanning trees in infinite graphs

Pascal Gollin

IBS Discrete Mathematics Group

IBS Discrete Mathematics Group

2019/10/29 Tue 4:30PM-5:30PM Room B232, IBS (기초과학연구원)

Given a cardinal $\lambda$, a $\lambda$-packing of a graph $G$ is a family of $\lambda$ many edge-disjoint spanning trees of $G$, and a $\lambda$-covering of $G$ is a family of spanning trees covering $E(G)$.

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.

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