arXiv subjects

Paul Knappe

Publications and source records attributed to Paul Knappe.

20 records · Page 2Linked to original sources

arXiv2019

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

We show that if a graph admits a packing and a covering both consisting of $λ$ many spanning trees, where $λ$ is some infinite cardinal, then the graph also admits a decomposition into $λ$ many spanning trees. For finite $λ$ the analogous question remains open, however, a slightly weaker statement is proved.

math.CO↗

arXiv2018

Circuits through prescribed edges

We prove that a connected graph contains a circuit---a closed walk that repeats no edges---through any $k$ prescribed edges if and only if it contains no odd cut of size at most $k$.

math.CO↗