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

October 29 Tuesday @ 4:30 PM - 5:30 PM

Room B232, IBS (기초과학연구원)

Speaker

Pascal Gollin
IBS Discrete Mathematics Group
https://dimag.ibs.re.kr/home/gollin/

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.

Details

Date:
October 29 Tuesday
Time:
4:30 PM - 5:30 PM
Event Category:
Event Tags:

Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum