4 papers
ErdÅs-Pósa property of -paths in unoriented group-labelled graphs
O-joung Kwon, Youngho Yoo
We characterize the obstructions to the ErdÅs-Pósa property of -paths in unoriented group-labelled graphs. As a result, we prove that for every finite abelian group and f…
Unavoidable pivot-minors in graphs of large rank-depth
Jungho Ahn, Kevin Hendrey, O-joung Kwon +1
Shrub-depth and rank-depth are related graph parameters that are dense analogs of tree-depth. We prove that for every positive integer , every graph of sufficiently large rank-d…
The ErdÅs-Pósa property for circle graphs as vertex-minors
Rutger Campbell, J. Pascal Gollin, Meike Hatzel +4
We prove that for any circle graph with at least one edge and for any positive integer , there exists an integer so that every graph either has a vertex-minor…
A coarse ErdÅs-Pósa theorem
Jungho Ahn, J. Pascal Gollin, Tony Huynh +1
An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic ErdÅs-Pósa theorem to induced packings of cycles.…